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TI-89 in MA206 - West-Point.ORG, The West Point Connection

1. 3 On the sending calculator select the Stats List Edi flash application a Select F 7 Flashapp to display the list of flash applications b Highlight the Stats List Edi application it may already be high lighted for example if its the only one there c Press F 4 to check mark the Stats List Editor application A small check mark should appear next to the application name 4 On the receiving calculator select the LINK menu by selecting 2nd VAR LINK Both calculators should now be in the VAR LINK screen 5 On the receiving calculator select the receive option a Select F3 LINK b Move the highlight to option 2 Receive c Press Enter The messages VAR LINK WAITING TO RECEIVE and BUSY should appear on the status line 6 On the sending calculator select the Send to TI 89 92 Plus option 87 a Select F3 LINK b Move the highlight to option 3 Send to TI 89 92 Plus c Press ENTER The message SENDING TISTATLE a progress bar and the BUSY indicator should be displayed on the receiving calculator 7 Wait until the screen clears on the receiving calculator about 75 seconds When the receiving calculators VAR LINK screen returns the transmission is complete For more information on installing flash applications see Transmitting Variables Flash Applications and Folders beginning on page 367 of the TI 89 and TI 92 Plus Guidebook E 4 Revision History This is a revision history of the procedure des
2. 1 newcommand acr 1 ac 1 index 1 newenvironment revision 3 par noindent textbf Revision 1 textit 2 3 1 relax 96269696969626262626962696969696969626 6262626262676767676762676262626262626262626969696969696 6 626262626267676767626767620202026 newcommand StatsLE textsl TI 89 Statistics with List Editor Mnewcommand Nphat Nensuremath Mhat p 33 newcommand ghat ensuremath hat q newcommand TIint ensuremath int 92 newcommand caret space def nCr 41 2 left begin array c 1 2 end array right def P 41 ensuremath cal P left 1 right def V 41 ensuremath cal V left 1 right def E 41 ensuremath cal E left 1 right def CI 41 2 ensuremath left 1 2 right 952696969696262626262626969696969696 66962626262676767676762676262626262626262626969696969696 6626262626262676767676267620202026 Xmakeindex 96269696969626262626962696969696962626626262626267676767676267626262626262626262626969696969626 626262626262676767676267620202626 o File defined by 89ab 90abc 91ab 92ab 93 Appendix G Acronyms CAS Computer Algebra System CDF Cumlative Distribution Function GUI Graphical User Interface MVUE Minimum Variance Unbiased Estimator NIST National Institute of Standards and Technology PDF Probability Density Function PMF Probability Mass Function USMA United States Military Academy 94 Appendix H Bibliography 1 A
3. 6 1 Arbitrary Random Variables 21 22 22 23 23 23 25 25 25 7 Point Estimates 28 8 Confidence Intervals 30 Lu wu md ded Buc 30 ee ias 32 MSN 35 8 4 TI 89Functons nh 36 9 Hypothesis Testing 37 38 DE 38 A 2 Features of TI 89 Basic Programs 39 A REE UN AR E ARS OL 39 Rk Haake eB Ae ede he dedi dedi OS 39 HT 39 39 40 40 43 43 43 43 46 46 46 66 67 67 67 13 68 68 70 B 1 Copying Programs from Another TI 89 71 B 2 Entering Programs in TI Graph Link 71 B 3 Extracting Programs from the Source of this Documen 71 B 4 Uploading Programs with Tl Graph Link 71 73 Cl Literate Programming ow x 9o a 73 C 2 ASCII Format for TI 89 Programs 73 C 3 Toolbars 0000008 8 75 E Upgrading a TI 89 Calculator for MA206 Probability and Statistics I Indexes 97 CT 97 I 2 Scraps Defined us vede V A 97 L3 Identifiefs estos adat A ARDAQAE BLS Blak dn dee 97 orem 98 List of Figures 21 A cautionary note with thanks to Cadet John Thompson TET 44 OS 44 ee Pe Ree 47 GAG hee hae hake a 48 oe beh oh hee a hak en 61 cea te Ak Bee ae ae es 61 D WARS hee Ta che 62 MEINES 62 List of Tables C 2 Greek letters in ASCII export files C 4 Special characters in ASCII export files 77 C 5 Upper case internatio
4. Initial conversion to SGML including only the chapter on upgrading the calculator 84 Appendix E Upgrading a TI 89 Calculator for MA206 Probability and Statistics E 1 Overview To load the TI 89 Statistics with List Editor flash application you need to load the Advanced Mathematics Software Operating System base code and then install the Statistics with List Editor application The TI manual indicates that it is about four times faster to do this from calculator to calculator than from desktop to calculator This discussion assume you have two TI 89 calculators one with the Advanced Mathematics Software and Statistics with Lists application in stalled and one which you are upgrading to that configuration and that you have a calculator to calculator link cable E 2 Installing the Advanced Mathematics Soft ware using another TI 89 1 Ensure both calculators have fresh batteries Warning A power loss or any other interruption during this oper ation will mean the receiving unit has to be reloaded using a computer 85 Ensure any data which is to be retained on the receiving calculator is backed up to another calculator or computer Warning This procedure will delete all user variables and reset the receiving calculator to its factory state This may include deleting flash applications Link the two TI 89s using the calculator to calculator cable as de scribed on page 366 of the TI 89 and TI 92 Plus Guide
5. NormCDF 42a 68 upper 47 63 67 lambda 57 58 14 General Index 89p filename 72 ASCII 73 74 autoaoff 41 81 binomial distribution 22 43 confidence interval 59 box plot 18 calculator sty filename 71 89 calculus functions 23 CAS 10 clev variable 61 clevel variable 65 combinations 20 combined standard uncertainty 31 comment strings 80 confidence interval 32 confidence level 33 Confidence Level variable 63 coverage factor 33 custom menu 39 expected value continuous distribution 24 discrete distribution 21 exponential distribution 25 confidence intervals 58 cumulative distribution 56 98 factorial 19 flash application 9 Gaussian distribution 26 histogram 17 hypergeometric distribution 22 46 cumulative distribution 51 probability mass function 49 literate program 73 lower limit variable 47 Lower Value variable 43 MA206 8 MA206 TXT filename 71 MA206PRO 89g filename 72 maximum sample 29 mean sample 28 median sample 29 minimum sample 29 n variable 23 43 49 52 61 65 Normal distribution 26 Number of Trials variable 63 Nuweb 73 82 83 89 Observed Successes variable 63 one variable statistics 29 p variable 43 PDF filename 89 90 permutations 20 plots box 18 histogram 17 Normal 26 probability 26 point estimates provided by interval estima tion functions 29 Poisson distri
6. RT3ebra Ca1c Fr3ml cT can Ue ah Einamid1 Probabilities Mum Trien E Frob success p E O O Lower Value oo fe Urker Value iE RAD RPFRDS FUNC Figure A 1 binomGUI input screen Fer Fir FE Far Rl3ebra catc Fr3milli cTean Ur Figure A 2 binomGUI output screen 44 NSTART92N NCOMMENT NNAME BinomGUI NFILE BINOMGUI 89P O Prgm NCON ARGS none Binomial probabilities NCON Compute interval probabilities NCON for a binomial distribution NCCO N USES TIStat binomCdf NCON Rev 1 2 21 JUN 02 NCON D Math Sci Mark Wroth local n p lo hi cdf Dialog Title Binomial Probabilities Request Num Trials n un Request Prob Success p p Request Lower Value lo Request Upper Value hi EndDlog If ok 1 Then expr lo gt lo expr hi gt hi expr n gt n expr p gt p lo gt statvars LowVal hi gt statvars UpVal n gt statvars n p gt statvars p TIStat binomCdf n p lo hi gt statvars Cdf format statvars Cdf 5 gt cdf string statvars LowVal gt lo string statvars UpVal gt hi string statvars n gt n string statvars p gt p Dialog Title Binomial Probability Text PC amp lo amp lt X lt amp hi amp amp cdf Text Text n n 45 Text p amp p EndDlog EndIf EndPrgm STOP92 o A 5 Hypergeometric Distribution A 5 1 Name hypergeo Compute probabilities related to a hypergeometric d
7. Section A 8 6 2 3 Exponential Distribution The Exponential distribution is not a separately defined probability distri bution in the Statistics with List Editor application Therefore all manipu lations of random variables with this distribution depend on manipulating the PDF directly user defined programs or on the use of known formulas The expcd function discussed in the Section A 9 expcdf reference page can be used on the TI 89 to compute probabilities related to expo nential random variables For A gt 0 it implements the analytic probability distribution function Ae x20 fx 0 otherwise 6 3 6 2 4 Normal Gaussian Distribution The Normal or Gaussian probability distribution is one of the pre defined distributions in the TI 89 Statistics with List Editor application Because 25 of its promenance in statistical applications there are a variety of built in functions for accessing and manipulating this distribution Computing Normal Probabilities There are two main methods for computing probabilities involving the Normal distribution the Normal Cdf function accessed from the F5 Distr menu of the TI 89 Statistics with List Editor application and with the Shade function also accessed from the F5 Distr menu of the TI 89 Statistics with List Editor application Both require the mean standard deviation and limits of the interval the Shade function in addition to computing the probability that
8. and 7 provide some additional insight into programming the TI 89 81 Appendix D Revision History This Appendix gives the revision history of this document as a whole Revision 15 0 2002 09 29 18 50 44 MarkWroth Recovering the master files from backup following a computer crash Adding and clarifying references to literate programming including specifically comments on the use of Nuweb Revision 14 10 2002 06 23 22 21 10 WrothMark Fixed a command typo Revision 14 9 2002 06 23 22 18 13 WrothMark Minor discussion of au toaoft Added some additional indexing commands Revision 14 8 2002 06 23 20 39 45 WrothMark Modified the definitions of the thebibliography and theindex environments to deal correctly with the bookmarks and table of contents by including entries in both places Revision 14 7 2002 06 23 20 23 40 WrothMark Added discussion of confi dence intervals Revision 14 6 2002 06 21 02 47 44 WrothMark Added comment lines to the beginnings of functions and programs giving their argument lists Added an example of manipulating an arbitrary PMF for a discrete random variable Converted the bibliography to a specially designed BibTEX format Added an experimental Tool Bar menu Added general discussion at the beginning of the document Added an example on the used of the calculator integration function to find the expected value using the definition 82 Revision 14 3 2002 06 18 21 06 11 WrothMark Fixed a ty
9. code implementing them See Appendix C for further details on the me chanics of this process A 1 General Notes on the Statistics with List Ed itor The TIStat applications belonging to the TI 89 Statistics with List Editor flash application need their own reference pages the application manual 10 does not describe how to use the applications from the Home screen although they are available from the CATALOG screen as well as from the MA206 program To some extent this document attempts to fill that gap at least with respect to the applications used in the basic probability and statistics course Students using the TIStat applications should note that most of them store their outputs to the statvars directory 38 A 2 Features of TI 89 Basic Programs A 2 4 Auto Alock It is a sometimes annoying feature of the TI 89 that when the user is placed in a dialog box the alpha lock is automatically turned on While this behavior is reasonable if the actual data being requested is a string But for many math programs including most or all of the ones defined by this document it means you must first press the a key to turn the a lock back off If this behavior really irritates you the Auto Alpha Lock Off program by Kevin Kofler available from www ticalc org can reportedly prevent it A 3 MA206 Custom Menu A 3 1 Name MA206 Set up a custom menu allowing easy access to functions com monly used in the bas
10. significance level or 100 1 a the confidence level The expression can be manipulated to make understanding how to find k easier P O kog lt 0 koo 1 a P kog lt 0 lt kog 1 a A pm lt lt k 1 a 0 p k gt EL 4 21 O 0 06 e do P k gt gt k 1 a P l a The numerical value of k depends on the distribution of the statistics involved in the confidence interval and on the desired probability a The conventional notation in this case is Z 2 z because of the assumption that the distribution involved is Normal because we are sampling from a Normal distribution X is Normally distributed and a 2 because to put a probability of a outside the confidence interval we need to put a 2 outside each end of the interval More specifically because we are dealing with distances away from the the mean of the distribution and are scaling those distance by the standard deviation of the distribution the k value in this case is based on a standard 33 Normal distribution Z one whose mean is zero and standard deviation is 1 To compute the numerical value we need to compute the value Z 2 such that P Z gt Za 2 a 2 With the TI 89 this value is easy to find Picking a 0 1 we can find xo os using the inverse Normal function to be 1 64485 Since the variance of X given that we know 0 is o n This confidence interval T X Zap 8 1 a 2 Jn gives a 10
11. Approx APPROXIMATE Dialog Title Normal CDF Request Lower Value lo Request Upper Value hi Request mu mu Request sigma NsigmaN EndDlog If ok 1 Then expr lo gt lo expr hi gt hi expr mu gt mu expr sigma gt sigma TIStat normCDF lo hi mu sigma gt cdf lo gt statvars lo hi gt statvars hi mu gt statvars mu sigma gt statvars sigma cdf gt statvars cdf 68 Dialog Title Normal CDF Text CDF amp string cdf Text Text Lower Value amp string lo Text Upper Value amp string hi Text Amux amp string mu Text sigma amp string sigma EndDlog EndIf setMode usrMode EndPrgm STOP92 o 69 Appendix B Installation This document assumes that you have successfully installed the TI 89 Statistics with List Editor application This may also have required you to install a newer version of the operating system itself If you need help with these procedures see Appendix E Depending on what you have available there are several possible ap proaches to the problem of installing the programs this document creates The obvious ones are Copy them from another TI 89 that already has them installed This is probably the easiest method provided you have access to another calculator that already has them Copying the programs is discussed briefly in Section B 1 and in the calculator documentation
12. Fig ure A7 or 0 2615 0 7385 from 1 PropZInt shown in Figure A 8 As discussed above the difference in the outputs is due to the implementing equations and the very small sample size chosen for the example A 11 4 TI 89 Implementation binomCI BINOMCI TXT 63 NSTART92N NCOMMENT NNAME BinomCI NFILE BINOMCI 89P O Prgm NCON ARGS none CI on a binomial proportion GUI NCONN Rev 2 0 2002 06 18 NCON D MathSci USMA Mark Wroth Local x n clev p hat z t1 t2 t3 lower upper string statvarsNx N Nx string statvars n gt n string statvars clevel gt clev Dialog Title Binomial Confidence Interval Request Observed Successes x Request Number of Trials n Request Confidence Level clev EndDlog 63 If ok 1 Then expr x gt statvars x expr n gt statvars n expr clev gt statvars clevel expr x gt x expr n gt n expr clev gt clev x n gt p_hat p_hat gt statvars p_hat invNorm 1 clev 2 gt z z root p_hat C1 p hat n z 2 4 n 2 gt t1l 1 z 2 n gt t2 p_hat z 2 2 n gt t3 t3 t1 t2 gt statvars lower t3 t1 t2 gt statvars upper format statvars lower 5 gt lower format statvars upper 5 gt upper Dialog Title Binomial CI Text CI amp lower amp amp upper amp Text Text Confidence Level amp string statvars clevel Text successes amp string x amp trials amp string n Text p hat amp format Statvars p_ha
13. addition the chi2gui will store the following user inputs to the indicated variables and will use the values in those variables as the default choices when it opens statvars n The sample size statvars ssdevx The sample standard deviation square root of the en tered sample variance statvars clevel The confidence level 65 A 12 3 Example Given a sample of size n 17 and a sample variance of 137 324 3 compute a 9576 confidence interval on the population variance 1 Begin at the Home screen 2 Enter the command chi2int 17 137324 3 95 1 and press Enter Tip Asa shortcut to entering the command name use the Catalog function and select the F4 User Defined tab Then select the desired function from the list 3 Read the confidence interval 76171 3 318080 on the resulting re quester Alternatively using the chi2gui to solve the same problem 1 Start the chi2gui by entering chi2gui O at the Home screen 2 Enter the values for n the sample variance and the confidence level in the open requesters 3 Selectthe desired confidence interval type from the drop down menu 4 Press Enter 5 Read the confidence interval 76171 3 318080 on the resulting re quester Note This is Example 7 15 from 4 However the use of the full accuracy of the Chi squared inverse function rather than the five significant figures available from a set of tables results in a slightly different answer than Devore obtains 6
14. for the necessary inputs Inputs x The value at which the CDF is to be evaluated n The sample size succ The total number of successes in the population pop The total number of elements successes and failures in the popula tion Outputs probability The CDF value A 7 4 Example To find the probability that a random variable from a hypergeometric distribution with a population size of 50 with 15 successes and a sample size of 10 has 5 or fewer successes 1 Enter hygeocdf 5 10 15 50 in the entry line of the Home window 2 Press Enter 52 3 The expression you entered and the answer 969998 will be dis played in the History Area Note If you enter all of the parameters using exact forms the calcula tor will display the exact answer in this case 2813126 2900135 Entering any parameter using a decimal form the 5 in the ex ample cause the calculator to provide the approximate answer A 7 5 TI 89 Implementation The CDF for the Hypergeometric can be implemented easily given the existence of a PDF function which correctly returns zero for values of x which violate the side conditions see HYGEOCDF TXT 53 NSTART92N NCOMMENT NNAME hygeoCdf NFILE HYGEOCDF 89P hygeoCd f x n succ pop Func NCON ARGS x n succ pop CDF for a Hypergeometric RV NCON USES hygeoPdf NCON Rev 1 1 NCON Mark Wroth Sigma ChygeoPdf i m succ pop i 0 x EndFunc STOP92 o We depend on the error checking
15. the interval This approach implies the need for a user manipulatable PDF PMF functions e Subtract the endpoint Cumlative Distribution Function CDF values Most easily executed at the Home entry line this approach implies the need for a user manipulatable CDF for each distribution e Create or find a calculator program which computes the interval probability Internally such a program may use either computation approach There is no theoretical reason to choose between these techniques Ide ally a student would master all of the different techniques and choose the technique appropriate to the particular problem Common practice in teaching the computation is to cover PDF based approaches but to emphasize CDF based approaches This fits well with the use of distribution tables and may be easiest for some students because of this connection At the same time the primary user interface for the probability com putations in the TI 89 TI 89 Statistics with List Editor is a program based Graphical User Interface GUI which allows the user to enter the distribu tion parameters and the ends of the interval While entry line functions are 12 also provided in the TI 89 Statistics with List Editor use of these functions from the entry line is essentially undocumented Consistency with the general approach of the TI 89 would appear to suggest GUl based inter faces are desirable This requires writing programs for the distributions wh
16. the random variable is in the interval draws the PDF and shades the area of interest Normal Probability Plots The F2 Plots menu includes the ability to create a normal probability plot of data in one of the lists To draw a normal probability plot 1 Start the TI 89 Statistics with List Editor application 2 Enter the data into a list variable 3 Select the Plots menu by pressing F2 Plots 4 Select 2 Norm Prob Plot 5 Fill out the resulting Norm Prob Plot requestor a Select an unused list variable at the Plot Number popup b Enter the name of the list variable containing the data for which the probability plot is needed in the List box c Select values for the remaining entries on the requestor The default values are probably acceptable 6 Select ENTER to close the requestor 7 Select the Plots menu by pressing F2 Plots 8 Select 1 Plot Setup 26 9 Select the plot variable containing the normal scores the name of this variable was chosen in the Plot Number popup of the Norm Prob Plot by highlighting it using the cursor keys and pressing F4 10 Display the plot by pressing F5 ZoomData 27 Chapter 7 Point Estimates The TI 89 calculates a variety of sample statistics that can be used as point estimators for various quantities The procedure for computing the most common of them is described above in Section 4 1 1 This procedure produces a dialog box showing the following sta
17. 0 1 a confidence interval for the mean of a Normal population whose standard deviation o is known This is the confidence interval that the TI 89 ZInterval function computes But we are working on the assumption that we know o the true pop ulation standard deviation Usually this will not be true if we know enough about the distribution to know its standard deviation we also al ready know its mean Because the situation where we are dealing with a population modeled by a Normal distribution with unknown mean u and standard deviation o is fairly common considerable thought has gone into how to find the appropriate values The approach starts with the random variable a A A OX 5 Jn This random variable has a Student s T distribution with n 1 degrees of freedom The T distribution is very similar to the standard Normal Z except that it has one parameter the number of degrees of freedom v The effect of this parameter is to define how much more variable than the standard Normal the T is the smaller v is the more variable the T distribution is If v oo the T distribution is the standard Normal For finite values of v the variance of the T is greater than 1 Reversing the process by which we explored the value of k we can find that for this case the interval SE S X k X k vu i 34 gives an interval whose confidence level 100 1 a is determined by the coverage factor k in the same way a
18. 6 A 12 4 TI 89 Implementation chi2int txt 67 START92 COMMENT NAME chi2int NFILE CHI2INT 89P chi2int n s2 clevel type Prgm NCON ARGS n s 2 clevel type Chi 2 CI type 1 on var 2 on SD NCON Rev 1 2 2002 06 15 NCON D MathSci USMA Mark Wroth local l u stsr n 1 s2 tistat invchi2 1 1 clevel 2 n 1 gt 1l n 1 s2 tistat invchi2 1 clevel 2 n 1 gt u CI on sigma 2 gt tstr If type 2 Then root 1 gt 1 root uw gt u CI on sigma gt tstr EndIf Dialog Title tstr Text Cint amp string 1 amp amp string u amp Text n amp string n amp S 2 amp string s2 EndDlog 1 gt statvars lower u gt statvars upper root s2 gt statvars ssdevx clevel gt statvars clevel EndPrgm STOP92 o A 13 Normal CDF A 13 1 Name normCDF is a user defined program that partially duplicates the function of TIStat normCdf The primary use for this function is to be pasted into the 67 Home screen command line and provide a GUI for data entry and results A 13 2 Usage A 13 3 TI 89 Implementation NORMCDF TXT 68 NSTART92N NCOMMENT NAME NormCDF FILE NORMCDF 89P O Prgm NCON ARGS none Normal probs GUI CC Compute normal probabilities NCON using the Gaussian Normal distn C C REQUIRES TIStat NormCDF NCON Rev 1 0 2002 06 15 NCON D MathSci USMA Mark Wroth Local lo hi mu sigma cdf getMode ALL gt usrMode setMode Exact
19. IFCDF 89P x a b Func NCON ARGS x a b CDF for a Uniform RV on a b NCON Rev 1 1 2002 06 15 NCON Mark Wroth If a lt b Then If x lt a Then Return 0 Elseif x b Then Return 1 Else x a b a EndIf Else Parameters a b EndIf EndFunc NSTOP92N o 95 A 9 expcdf A 9 1 Name expcdf Evaluate the CDF of an exponentially distributed random vari able A 9 2 Description This function implements the CDF for an exponentially distributed random variable with parameter A Such a random variable has PDF TO Ae A 3 A 9 3 Usage Inputs x The value of the random variable at which the CDF is to be evaluated A The parameter of the distribution A is one over the mean of the distrib ution Outputs cdf Cumulative probability the probability that the random variable is less than or equal to the supplied x If an invalid parameter A is supplied an error string is returned rather than a numeric result A 9 4 Example To compute the probability that an exponentially distributed random vari able with mean 5 is less than or equal to 3 1 Enter expcd 3 1 5 in the entry line of the Home window 2 Press Enter 56 3 The expression you entered and the answer 451188 will be dis played in the History Area Note If you enter both parameters using exact forms the cal culator will display the exact answer in this case 1 e 5 Entering either parameter using a decimal form the 3 in the
20. The TI 89 Calculator in the Basic Probability and Statistics Course LTC Mark B Wroth Department of Mathematical Sciences United States Military Academy West Point NY 10996 Revision 15 1 September 29 2002 This document may be freely reproduced as a complete document In structors using it as part of their course material are requested to notify the author at mark wrothQus army mil This is Revision 15 1 produced from ti89ma206 w on September 29 2002 The cartoon in Figure is reproduced with the permission of the cartoonist Cadet John K Thompson USMA 2004 Contents 1 Introduction 8 LI Why This Documental 4 x oh a 8 12 How to Use This Document 9 2 General Issues in Learning Probability and Statistics Armed with an Advanced Calculator 10 as A A a ee ee 22 Interval Probabilities 12 2 3 Standardized Random Variables 13 3 Calculator Tips 15 SA AN 15 4 Descriptive Statistics 16 4 1 Numerical Methods 16 quer 16 PEE E NUR M A E 17 4 2 1 Histograms a a oaoa 17 E BOX Pl lS A 18 19 DAL COUNTING cock e xe xo RO doy e AC Regn ue y DER MEE HS 19 REO Ux XO WC NCC NCC E A 19 bal PACtOrials 4 amp 3 dodo de do c Sedo eR DER HE 19 5 2 2 Permutations c r 20 5 2 3 Combinations xo o ROC REOR XO 3 20 n 6 1 Discrete Random Variables 21
21. Upload them from a personal computer This is fairly straightfor ward provided you have a computer and the necessary connecting cable This approach is discussed in Sections B 2 entering programs via TI Graph Link B 3 importing programs from this document and B 4 actually uploading the programs Type them directly into the calculator This approach is always fea sible but is also the most painful since the TI 89 is not exactly set up for the rapid entry of text If you need to take this approach you will need to read at least parts of Section C 2 which discusses the format in which the programs are shown in this document 70 B 1 Copying Programs from Another TI 89 B 2 Entering Programs in TI Graph Link Typing the programs in this document into TI Graph Link is fairly straight forard if you are already familiar with programming the TI 89 You will need to review Section C 2 to understand the conventions used in the ASCII format programs B 3 Extracting Programs from the Source of this Document To extract the programs from the source of this document ti89ma206 w 1 Process the source of this document ti89ma206 w with Nuweb by commanding nuweb ti89ma206 w This will produce in addition to several other intermediate files a series of text files such as MA206 TXT The a list of the output files produced is in Section I 1 note that it includes files such as calculator sty that you would not want to upload B 4 Up
22. a section discussing the used of simulation on the calculator with particular reference to the simulation of sampling experiments and computation of test statistics or confidence intervals e Extend the CI functions to allow computations on a sample provided as a list similar to the TIStat functions 100
23. access to functions related to computing confidence intervals MA206 TXT 42b Title Intvl Item TIStat zInt Item TIStat tInt Item TIStat zInt 1P Item BinomCI Item Chi2GUI o File defined by 40ab 41ab 42abc Finally the Functions menu provides command line access to some of the functions underlying the other menus specifically including the PDF and CDF functions MA206 TXT 42c Title Functions Item TIStat binomPdf Item TIStat binomCdf Item ma206 hygeoPdf Item ma206 hygeoCdf Item ma206NexpCdf Item ma206NunifCdf Item TIStat normCdf Item Chi2Int 42 EndCustm CustmOn EndPrgm NSTOP92N o File defined by 40ab 41ab 42abc A 4 Binomial Distribution A 4 1 Name binomGUI TIStat binomCdf These GUIs compute the probability that a binomial random variable lies in the specified closed interval The binomGUI program provides access to the binomCdf program from the Home command line A 4 2 Usage Inputs n The number of trials p The probability of success on each trial Lower Value The lower endpoint of the interval over which the binomial probability is desired Upper Value The endpoint of the interval over which the binomial prob ability is desired The input dialog from binomGUI is shown in Figure A 1 The dialog box from the Binomial CDF application is similar Outputs Example A 4 3 TI 89 Implementation BINOMGUI TXT 43 43 Fir Fie FE Far
24. agemode UseOutlines hypertexnames false o File defined by 89ab 90abc 91ab 92ab This environment will allow us to write a BibTEX bibliography as part of this file It will be written to disk as ti89ma206 bib and then can be processed using the normal BibTEX commands calculator sty 90c newwrite verbatim out newenvironment bibtex bsphack immediate openout verbatim out jobname bib let do makeother dospecials catcode M active def verbatim processline immediate write verbatim out the verbatim line verbatim start immediate closeout verbatim out esphack o File defined by 89ab 90abc 91ab 92ab 90 Likewise we modify the definition of the thebibliography environment to cause it to make an appropriate table of contents and hence PDF book mark entry calculator sty 9la setlength bibindent 1 5em renewenvironment thebibliography 1 list biblabel arabic c enumiv settowidth labelwidth biblabel 1 leftmargin labelwidth advance leftmargin labelsep Gopenbib code usecounter enumiv let p enumiv Gempty renewcommand theenumiv arabic c enumiv sloppy clubpenalty4000 clubpenalty clubpenalty widowpenalty4000 sfcode n def Gnoitemerr latexG warning Empty thebibliography environment endlist let openbib code empty o File defined by 89ab 90abc 91ab 92ab This change redefines the index environment so that it too
25. art Lbl unif ma206 unifGUI Goto start Lbl exp ma206 expGUI O Goto start Lbl nml ma206 normCDF Goto start Lbl clear ClrHome Goto start Lbl quit EndPrgm STOP92 o C 4 Random Notes C 4 1 Help Strings The catalog screen reports as help information the first comment line after the Prgm or Func line of the program This line can be longer than an output line it will be wrapped into a dialog box when the user presses F1 However only the first few characters will be displayed at the bottom of the catalog screen C 4 2 Unavailable Functionality It does not appear to be possible to insert a function prototype i e to give variable names for arguments to a function to be pasted into the entry line using a custom menu It does not appear possible to allow a variable number of parameters to be passed to a function or program or to branch within a function or program based on the number of supplied parameters 80 C 4 3 Automatic Alpha Lock The TI 89 automatically turns on the alpha lock when a dialog box is created using the Request command While this would be convenient if strings were the expected input itis less so in these applications However Ido not know a way to turn the alpha lock back off or to keep it from turning on the Auto Alpha Lock Off program by Kevin Kofler available from www ticalc org can prevent this behavior C 4 4 Additional Programming References References 6
26. ary discrete proba bility mass functions If the PMF can be described algebraically or by a function defined in the 11 89 the summation operator can be used to compute quantities defined based on a summation over the entire PME An example of such a quantity is the expected value To compute the expected value of the function defined by TIStat binomPdf which happens to be the binomial distribution using the definition n E X xp x i 0 we could enter into the calculator Y x TIStat binomPdf 5 2 x x 0 5 For this distribution this is easily computed to be np 1 confirming the result given by the calculator Unfortunately the calculator does not handle the general expression that is it will not compute the formula for the expected value in general 21 Fora more general arbitrary distribution enter the values of the random variable into one list and the associated probabilities into the correspond ing positions of a second list Entering the values from 4 page 110 into the lists named x and p we can compute 24x 1 1 p 1 1 0 7 finding 4 57 the same result obtained by Devore This notation parallels the traditional notation Y xp i 0 6 1 2 Binomial Distribution The Binomial probability distribution is one of the pre defined probability distribution in the TI 89 Statistics with List Editor application It is ac cessed via the F5 Distr menu using either the B Binomial Pdf or C Binomial Cdf men
27. asted into the entry line Revision 9 17 June 2000 MBW Added appendix showing symbols and procedure for normal probability plots Included RevHistory in the hyper geo program listing as an experiment as set up in the print version the data remains in the SGML file but is suppressed in the printed version exactly as hoped Revision 8 15 June 2000 MBW Added procedures for graphical descrip tive measures Some update of other areas Revision 7 14 June 2000 MBW Added documentation for the hypergeo program and added the use of the callout element for documentation Revision 6 13 June 2000 MBW Completed reference page entries for the four functions documented in this paper including adding examples Moved the function definitions to the reference pages rather than in the general discussion for better parallelism with the pre defined functions 83 Revision 5 13 June 2000 MBW Added reference entries for hypergeomet ric distribution The reference entries for the other defined programs still need to be done Revision 4 12 June 2000 MBW Added function definitions for hypergeo metric distribution Revision 3 8 June 2000 MBW Added definitions for the uniform and exponential CDFs as example user defined functions Revision 2 4 June 2000 MBW Added basic information on the functions built in to the statistics application Very limited coverage of the sections on estimation and hypothesis testing Revision 1 3 June 2000 MBW
28. book On both calculators select the LINK menu a Select 2nd VAR LINK b Select F 3 LINK On the receiving calculator select Receive Product Code a Cursor down until option 5 Receive Product Code is high lighted b Press ENTER c A warning message will display Press ENTER to continue or ESC to abort On the sending calculator select Send Product Software a Cursor down until option 4 Send Product SW is highlighted b Press Enter c A warning message will display Press ENTER to continue or ESC to abort After a short pause about five seconds the receiving calculator will display a status message and progress indicator Wait until the display clears about six minutes When the display clears the transfer is complete Warning 86 Interrupting the transmission will result in the receiving calculator becoming inoperable until it is reloaded from a computer 8 Reload any backed up data to be retained on the receiving calculator For more information on installing base code updates see Upgrading Product Software Base Code beginning on page 373 of the TI 89 and TI 92 Plus Guidebook E 3 Installing the Statistics with List Editor Flash Application Using Another TI 89 1 Link the two TI 89s using the calculator to calculator cable as de scribed on page 366 of the TI 89 and TI 92 Plus Guidebook 11 2 On the sending calculator select the LINK menu by selecting 2nd VAR LINK
29. bution 23 Pop variable 22 52 pop variable 50 52 Pop size variable 47 probability variable 50 52 probability distributions arbitrary continuous 24 arbitrary discrete 21 binomial 22 43 exponential 25 hypergeometric 22 Normal 26 Poisson 23 uniform 25 probability plot normal 26 program group 72 quartile sample 29 random interval 32 s2 variable 65 99 sample size 29 Sample size variable 47 significance level 33 size sample 29 standard deviation sample 28 Statistics with List Editor 38 statvars clevel variable 65 statvarsMower variable 61 65 statvars n variable 65 statvars ssdevx variable 65 statvars upper variable 61 65 Student s T distribution 34 Succ variable 23 52 succ variable 49 52 Successes variable 47 TI Graph Link 70 72 ti89ma206 w filename 71 total sample 28 type variable 65 Type A evaluation of uncertainty 31 Type B evaluation of uncertainty 31 uniform distribution 25 cumulative distribution 54 upper limit variable 47 Upper Value variable 43 user help 80 x variable 49 52 60 ZoombData 18 To Do e Convert all of the input and output variable lists to varlists e Add GUI s callable by the MA206 menu for the remaining TI 89 functions commonly used e Index the various distributions and add cross references between the discussion of usage and the relevant implementing function e Add
30. cribed in this Appendix i e of the procedure for upgrading the TI 89 Revision 1 2 3 June 2000 MBW Conversion to SGML as a chapter in a DocBook book Revision 1 1 1 June 2000 MBW Minor edits after testing the procedunes Revision 1 0 30 May 2000 MBW Initial version 88 Appendix F Document Production Notes This document is produced using Nuweb a literate programming appli cation originally by Preston Briggs and now maintained on SourceForge The PDF file is produced using pdfET X customizations for this document are in the file calculator sty shown below The intitial part of the style file is identification of the KTFX package calculator sty 89a NeedsTeXFormat LaTeX2e ProvidesPackage calculator 2002 06 23 MA206 Calculator Notes o File defined by 89ab 90abc 91ab 92ab Now we load the packages that are used in the document calculator sty 89b usepackage pxfonts usepackage alltt graphicx longtable makeidx RCS verbatim usepackage f hyperref usepackage acronym usepackage multicol o File defined by 89ab 90abc 91ab 92ab This records the revision of the document that produces this 89 calculator sty 90a RCS Revision 15 1 RCS Date 2002 09 29 20 19 10 o File defined by 89ab 90abc 91ab 92ab Now we set up the PDF annotations calculator sty 90b hypersetup pdftitle TI 89 in MA206 pdfkeywords probability statistics calculator TI 89 pdfp
31. design essentially the same inputs and provide the same outputs they are adapted to different user interfaces and slightly different underlying equations as discussed above In general use binomCI is slightly preferable it is definitely preferred when n is not large Inputs x Number of observed successes 60 n Number of trials clev The desired confidence level Dbserued Successes E Humber of Trials Confidence Level Enter 0K ESC CAMCEL Figure A 5 BinonCI input screen Fix Fur FE Far Fr List CaTc Diskr Tests Inks ht i Froportion Z Interug yi Succesen x ET n C Lover Enterz K ESC CANCEL TYFE CENTERISOK AND CESCISCAMNCEL Figure A 6 1 PropZInt input screen Outputs statvars lower Lower end of the CI statvarslupper Upper end of the CL 61 Fir Fie FE Fer RT3ebra Ca1c Fr3ml CcTcan Ue Confidence Lengt E successes 1 rins Pohak En Enter 20K ESC CAMCEL mazte binanmci EFE AD AUTO FUN Figure A 7 BinonCI output screen 270806047 E 260074 zin RAD AUTO FUNC Figure A 8 1 PropZInt output screen 62 Example To compute a 90 confidence interval on the population proportion given 5 successes out of 10 trials enter Observed Successes 5 Number of Trials 10 Confidence Level 9 as shown in Figure for the binomCI program or Figure for the 1 PropZint program The results a CI of 0 28476 0 71524 from binomCI shown in
32. e not so some ability to use them is probably a good idea More important from the perspective of the course material is that the ma nipulations to standardize the Normal random variable are the basis of the manipulations by which we derive the formulas for confidence intervals So understanding how to standardize the normal random variable is a lead in to the material on confidence intervals Finally statistical packages including the TI 89 s advanced statistics functions frequently state hy pothesis test results in terms of standardized test statistics Understanding the test results depends to some extent on understanding the normalized 13 versions of the statistics Having said that however this document largely focuses on the direct manipulation of the random variables directly of interest in the problem Standardized random variables are a special case of this focus 14 Chapter 3 Calculator Tips 3 1 Split Screen The calculator can split the main screen into two halves displaying two independent applications This is especially useful for working at the Home screen while keeping the TI 89 Statistics with List Editor application accessible To split the screen go to the Modes menu and set Split 1 App and Split 2 Appto the two applications you want to use Obvious candidates are Home and Stats List Editor Then set Split Screen to the mode you want Left Right is probably the preferable option if the list editor is o
33. e of the standard plot types available To create a histogram of data 1 Enter the data into a list variable Select F2 Plots to bring up the Plots menu Select 1 Plot Setup Select F1 Define 2 3 4 Highlight a plot line 5 6 Select Plot Type on the popup menu select 4 Histogram 7 Enter the name of the list variable containing the data in the x box 8 Enter an appropriate width for the histogram intervals in Hist Bucket Width 17 9 Ensure the NO option is selected in the Use Freq and Categories popup 10 Select ENTER 11 Select F5 ZoomData 4 2 2 Box Plots A basic box plot is one of the standard plot types available 1 Enter the data into a list variable Select F2 Plots to bring up the Plots menu Select 1 Plot Setup 2 3 4 Highlight a plot line 5 Select F1 Define 6 Select Plot Type on the popup menu select 3 Box Plot 7 Enter the name of the list variable containing the data in the x box 8 Ensure the NO option is selected in the Use Freq and Categories popup 9 Select ENTER 10 Select F5 ZoomData The F3 Trace function allows easy examination of the particular values included in the plot 18 Chapter 5 Basic Operations 5 1 Counting The TI 89 computes several basic functions useful for counting problems For most of these operations there are two or three different ways to access the same calculator function e Select the function
34. ell within the capability of the student it can also be solved as f 0 15 e 0 15 x 0 5 x 0 5 00 giving the result 7 16667 Tip The TI 89 exponential operator e C is not the letter e it is entered using the x key Variance Finding the variance of an arbitrarily defined continuous random variable can be accomplished by applying the definition of variance For simply defined functions e g the Exponential distribution this is easily accom plished with the Integrate function from the HOME F3 Calc menu The computational formula V X ECC E X 24 can be applied by integrating to find the expected value of X this may not be easier than applying the definition directly Defining the PDF or the CDF as a TI 89 function allows it to be used in subsequent calculations Examples of reasonable definitions are given for some of the probability distributions used in the basic probability and statistics course discussed below 6 2 2 Uniform Distribution The Uniform distribution is not a separately defined probability distribu tion in the Statistics with List Editor application Therefore all manipula tions of random variables with this distribution depend on manipulating the PDF directly user defined programs or on the use of known formulas The cumulative distribution function can be defined as a TI 89 function for convenience in calculation An example of such a definition is shown in in the uni fcdf reference page
35. erial in 14 8 1 Purpose of Interval Estimates The disadvantage of point estimates is that in isolation they provide no in formation about the accuracy of the estimate Merely from a point estimate that say the average height of a randomly chosen student is 70 inches the reader cannot tell if this value is precisely known or only very approxi mately known Experimental scientists have been dealing with this issue for many years and a variety of conventions for dealing with it have been tried For example one approach is to quote only the number of significant figures that are accurately known 70 is different than 70 0 is different than 7 x 10 While this can be a convenient shorthand it is counterintuitive in that from a mathematical sense all three of those representations express exactly the same number It is also problematic in that there is no easy way to express the idea that I m pretty sure the value is between 68 and 72 an uncertainty that does not fall neatly into a power of ten This general concern leads to expressing a measurement as a point es timate plus or minus some value that expresses the uncertainty assigned 30 by the experimenter to the value This is the approach commonly taken by National Institute of Standards and Technology NIST in reporting its experimental results and is probably familiar to the student from course work in the physical sciences NIST s stated policy 8 is to express the combined
36. example cause the calculator to provide the approxi mate answer A 9 5 TI 89 Implementation The expcdf function wraps a simple call to the usual mathematical de finition inside two tests The first of these tests checks that the required parameter is greater than zero as required by the definition of the func tion The second test checks whether the input value x is greater than or less than zero branching to the two piecewise definitions of the CDF depending on the result Both tests use the where function which is in essence a simple branching structure EXPCDF TXT 57 NSTART92N NCOMMENT NAME expCdf FILE EXPCDF 89P x lambda Func NCON ARGS x lambda CDF of an exponential RV NCON with parameter lambda NCON Rev 1 1 2002 06 15 NCON D MathSci USMA Mark Wroth when lambda gt 0 when x gt 0 1 e C lambda x 0 lambda must be gt 0 EndFunc STOP92 o 57 A 10 Exponential Probability GUI A 10 1 Name expgui Produce confidence intervals on the variance or standard devia tion of a Normal random variable A 10 2 Usage A 10 3 TI 89 Implementation EXPGUI TXT 58 NSTART92N NCOMMENT NAME expGUI FILE EXPGUI 89P O Prgm NCON ARGS none Exponential probabilities GUI NCON Rev 1 0 2002 06 15 NCON D MathSci USMA Mark Wroth Local lo hi MlambdaN cdf usrmode getMode ALL N NusrMode setMode Exact Approx APPROXIMATE Dialog Title Exponen
37. from a menu usually the Math menu accessed with the 2nd MATH key e Type the name of the function in the Entry Line using the alphabetic keys or a menu pick from a custom menu e Add the function to the Entry Line using the CATALOG Functions defined from flash applications such as Statistics with List Editor and user defined functions are also available through the CATALOG function e Add the function to the entry line using the Var Link menu 5 2 Counting Techniques 5 2 1 Factorials The factorial function is accessed with the postfix operator which can be entered from the keyboard using the 2nd CHAR function or from the 2nd MATH7 Probability menu 19 It is also found on the Counting menu of the MA206 custom menu 5 2 2 Permutations The permutations function can be accessed with the function nPr func tion This can be accessed via the 2nd MATH 7 Probability nPr menu pick It is also found on the Counting menu of the MA206 custom menu 5 2 3 Combinations The combinations function can be accessed through the nCr function This can be accessed via the 2nd MATH 7 Probability nCr menu pick or by typing the function name in the entry line It is also found on the Counting menu of the MA206 custom menu 20 Chapter 6 Random Variables and Probability Distributions 6 1 Discrete Random Variables 6 1 1 Arbitrary Random Variables List operations used to examine and manipulate arbitr
38. g interval estimation other than the functions used for calculating sample statistics is the F7 Ints menu which includes functions for Z and T based confidence intervals on the mean among others These functions allow the interval to be calculated directly from sample data or from previously computed sample statistics The F5 Distr menu s2 Inverse submenu includes functions for computing the critical values of the Normal Student s T and x distribu tions Tip The various inverse functions ask for the AREA proba bility at which the inverse is to be calculated This area is the probability that the random variable is less than the returned inverse value This is consistent with the general definition of a CDF However the critical values of a distribution are defined in terms of the probability that the random variable is greater than the critical value The translation between the two is of course that the area above the critical value is 1 minus the area the inverse function is expecting This difference can be ignored by taking the absolute value of the result ing critical value if the distribution is symmetric around zero Because this relationship does not hold true for distribution not symmetric about zero i e the x distribution or the general normal distribution relying on this property can lead the student into mistakes The5 1 PropZInt menu can be used to calculate confidence intervals on the population propor
39. ic probability and statistics course A 3 2 Description This program sets up a TI 89 custom menu which allows function names to be easily inserted into the Entry Line Tip Function and program names can also be easily pasted into the Entry Line by using the CATALOG key Once in the Catalog window pressing F3 Flash Apps will bring up a list of the functions installed by any flash applications and F4 User Defined will bring up a list of user defined functions Tip When a function has been highlighted in either the F3 Flash Apps or F2 Built in panes of the Catalog window pressing F1 Help will bring up a terse description of the inputs for the function 39 A 3 3 Usage Inputs This program has no inputs Outputs This program reconfigures the custom menu of the TI 89 It has no other outputs Example A 3 4 TI 89 Implementation This and other programs defined by this document are shown in the form exported by the TI 89 Graph Link program Copies of the ASCII version of the program are found in the output directory and can be imported into Graph Link MA206 TXT 40a NSTART92N NCOMMENT NAME MA206 NFILE MA206 89P O Prgm NCON ARGS none Set up MA206 menu NCON Program to set up an MA206 custom menu NCCO N Rev 3 4 23 JUN 02 NCON D MathSci USMA Mark Wroth Custom o File defined by 40ab 41ab 42abc The Tools menu is used for functions that manipulate the calculator itself The MA206 en
40. ich are not included in the Statistics with List Editor application For MA206 this would include the Hypergeometric Uniform and Exponen tial distributions The 11 89 allows the student to approach the calculation of interval probabilities any of the above ways given the availability of either exist ing programs or basic programming skills for the third approach To help gain understanding it may be a good idea for students to focus on one method and ensure it is mastered If GUI based programs are available for all of the distributions of interest focusing on this technique is likely to be the easiest 2 3 Standardized Random Variables The use of the calculator largely eliminates the need to use traditional probability tables Since being able to use the standard normal probability tables is one of the main ways the use of a standardized random variable is presented eliminating the need to use the tables at all also eliminates one of the major uses of standardized variables It is tempting to simply ignore the topic completely if the student has adequate calculator skills However there are several reasons to understand the basic manip ulations surrounding standardized random variables and the standard normal distribution in particular Perhaps least important is the fact that traditional tables while in some sense obsolescent as calculators with ba sic probability functions become more common are still available when calculators ar
41. ion of the locally produced functions and programs is discussed in Appendix C 1 2 How to Use This Document This document is generally divided into three main parts ChapterD deals with topics that affect how the course is structured and overall strategies for using the calculator in a probability and statistics course Chapters through 9 discuss the major lesson blocks in MA206 Finally the appen dices provide additional details on specific topics Appendix A Program and Function Reference may be of special in terest as it gives use notes for the calculator programs defined in this document It also gives the complete text of the programs in ASCII form and provides some discussion of selected programs from the TI 89 Statis tics with List Editor application LA flash application is an additional software package loaded into the TI 89 to provide specialized additional capabilities MA206 uses the TI 89 Statistics with List Editor flash application available from the Texas Instruments web site 9 Chapter 2 General Issues in Learning Probability and Statistics Armed with an Advanced Calculator 2 1 Use of Graphing Calculators in Teaching and Learning Mathematics It appears reasonable to believe and there is some research evidence to sugges that how instructors model and require the use of the calculator strongly affects how students make use of the calculator This is especially significant if the capabilitie
42. is appropriately entered into the table of contents and list of bookmarks calculator sty 91b renewcommand indexname General Index from report cls renewenvironment theindex begin multicols 2 let item idxitem end multicols renewcommand idxitem par hangindent 40 p renewcommand subitem idxitem hspace 20 p renewcommand subsubitem idxitem hspace 30 p renewcommand indexspace par vskip 10 p plus5 p minus3 p relax renewcommand see 2 emph seename 1 renewcommand hyperpage 1 04113 91 File defined by 89ab 90abc 91ab 92ab The following macros are used for simplicity in writing calculator sty 92a newcommand key 1 Ntexttt 71 newenvironment Note 1 begin quotation begin center Note end center noindent end quotation newenvironment Warning begin center Warning end center begin quotation noindent end quotation newenvironment tip begin quotation noindent textbf Tip end quotation newenvironment varlist begin description renewcommand key 1 item texttt 1 index 1 variable end description o File defined by 89ab 90abc 91ab 92ab calculator sty 92b newcommand df n 1 textit 1 index 1 newcommand app 1 textit 1 index 1 newcommand fname 1 texttt 1 index 1 filename newcommand guimenu 1 texttt 1 newcommand program 1 texttt
43. istribu tion specifically the probability that a hypergeometric random variable lies between two constants a and b inclusive A 5 2 Usage Description hypergeo is a program which prompts the user for the parameters of a hypergeometric distribution and the endpoints of an interval and then computes the probability that the random variable lies in that interval The hypergeometric distribution models a situation where a sample is taken from a finite population consisting of a fixed number of successes and failures without replacement The random variable is the number of successes drawn in the sample The format of the program is intended to be similar to the format used in the Statistics with List Editor application A 5 3 Usage The hypergeo program creates a requester that prompts the user for the necessary inputs and displays its outputs in another requester Inputs The input requester for hypergeo is shown in Figure A 3 46 SIEHE ER RERO Sample size For size Success Toler limit urrzr limit Ent rzDk ESC CANCEL d TYFE CENTERISOK AND CESCI CAMCEL Figure A 3 hypergeo input screen Sample size The size of the sample drawn Pop size Thetotal size ofthe population from which the sample is drawn Successes The number of successes in the population lower limit The lower limit of the interval for which the probability is desired upper limit The upper limit of the interval for which the probability is desi
44. l program to execute commands NCON directly Lbl start ToolBar Title Item Item Title Item Item Item Item Item Tools Exit quit Clear clear Distr Binomial binomial Hypergeo hyg Uniform unif Exponential exp Normal nml EndTbar Lbl binomial ma206 binomGUI Goto start Lbl hyg ma206 hypergeo 76 XlockX check block from to up down leftarrow uparrow downarrow left right shift None N cent pound starburst yen split section a_ lt lt Lnot NCRON Xe NEN ZN NIN AS para NN NEN VIN NON gt gt The LOCK character The CHECK mark char The centered block char block right arrow block left arrow block up arrow block down arrow left arrow up arrow character down arrow character big block left arrow big block right arrow shift up arrow character ellipsis cent character pound sterling starburst character yen character split vertical bar character section character feminine ord character double left arrow character logical not character registered mark character superscript minus character superscript plus character superscript 2 square superscript 3 cube superscript 1 inverse paragraph symbol dot mark superscript x character superscript 1 character masculine ord character double right arrow Table C 4 Special characters in ASCII export files 77
45. lan Agresti and Brent Coull Approximate is better than exact for interval estimation of a binomial proportion The American Statistician pages 119 126 1998 Cited in 4 2 Preston Briggs and Marc W Mengel Nuweb version 1 0b1 A simple literate programming tool 2002 version 1 0b1 was released 24 Feb ruary 2002 An older version is available as a Windows executable from 3 Gail Burrill Jacquie Allison Glenda Breaux Signe Kastberg Keith Leatham and Wendy Sanchez Handheld Graphing Technology in Sec ondary Mathematics Research Findings and Implications for Classroom Practice Texas Instruments 2002 Prepared through a grant to Michi gan State University 4 Jay L Devore editor Probability and Statistics for Engineering and the Sciences Duxbury Press Belmont CA 5th edition 1999 5 David Knellinger MA 206 Probability and Statistics Department of Mathematical Sciences Instructional Memorandum 206 1 27 May 2002 6 Tom Mount TI 89 92 Basic Programming Manual Downloaded from http www ticalc org pub text misc on 19 JUN 02 95 7 Tom Mount 1189 92 Advanced Programming Manual 2001 Down loaded from http www ticalc org pub text misc on 19 JUN 02 8 Barry N Taylor and Chris E Kuyatt Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results National In stitute of Standards and Technology Gaithersburg MD September 1994 9 Texas Instruments Advanced Mathe
46. loading Programs with TI Graph Link Before beginning upload of the programs to the calculator create a folder on the calculator in which the programs will be stored This document and the MA206 custom menu assume that the programs will be stored in ma206 Make this folder current on the TI 89 1 Start the TI Graph Link software 2 Load the program into TI Graph Link 71 a Import the text file into Graph Link by selecting Tools then Import ASCII Program Select the appropriate text file in the requester that appears and click OK This will import the program into Graph Link b Load the 89p file into TI Graph Link by selecting File then Open and selecting the desired file from the resulting requester 3 Send the program to the calculator using Graph Link following the instructions in the Graph Link user manual page 7ff If you have access to the programs in the from of a TI 89 program group usually named MA206PRO 89g they can be uploaded as a single entity Otherwise you will have to import each of them individually and send them to the calculator 72 Appendix C Programming Notes C 1 Literate Programming Literate programming is a method of creating a computer program such that both the documentation of that program and the actual source code can be presented to human readers in a manner intended to make the program as easy to understand as possible and correctly record the actual program as presen
47. make this computation In fact if we did we would not need to since the whole point of the exercise is to estimate 0 knowing its value would mean that we were done But for some practical cases we can proceed anyway Suppose we are sampling from a Normal population and assume for the moment that we know 0 and are trying to estimate u The obvious estimator for u is X since that statistic is the Minimum Variance Unbiased Estimator MVUE for u If the underlying population is Normally distributed X is also Normally distributed with X u and V X 0 n Then P X 0z lt u lt X 0x isjust the probability that a Normal random variable is within one standard deviation of its mean or about 68 We formally express this by saying that the interval X ox X ox is a 68 confidence interval for u More generally we would say that it is a 100 1 a confidence interval with a x 32 32 Conventionally in order to allow us to choose probabilities other than 68 we add a coverage factor k to the definition P kog lt 0 lt koa P X kog lt u lt X kog By choosing the coverage factor k appropriately we can make a any probability we want to While the choice of k 1 is suggested for the general reporting of experimental uncertainty by NIST other choices are conventional as well Usually these other choices are expressed not by defining values of k but by defining the resulting levels of either a the
48. matics Software This is an overview page for the AMS upgrade 10 Texas Instruments Statistics with List Editor http www ti com calc flash pdf statsle pdf This is the users guide for the Statis tics with List Editor application 11 Texas Instruments TI 89 and TI 92 Plus Guidebook for Advanced Math ematics Software Version 2 0 This is the updated manual for the Ad vanced Mathematics Software it replaces the manual included with the calculator 12 Texas Instruments Inc TI GRAPH LINK for Windows for the TI 89 Condensed Guidebook 13 Unknown ASCII conversion codes for ASCII calculator program code Downloaded from http www ticalc org pub text misc on 19 JUN 02 The only indication of authorship is Last Update 12 Mar 96 SLR at the end of the file 96 Appendix I Indexes 11 Files Written BINOMCI TXT Defined by 63 BINOMGUI TXT Defined by 43 calculator sty Defined bys 89ab 90abc 91ab 92ab chi2int txt Defined by 67 EXPCDF TXT Defined by 57 EXPGUI TXT Defined by 58 HYGEOCDF TXT Defined by 53 hygeoPdf txt Defined by 50 hypergeo txt Defined by 47 MA206 TXT Defined bys 40ab 41ab 42abc MA206CMD TXT Defined by 75 NORMCDF TXT Defined by 68 unifcdf txt Defined by 55 1 2 Scraps Defined I3 Identifiers chi2int 67 clevel 63 67 expCdf 42c 57 expGUI 42a 58 75 97 hygeoCdf 42c 53 hygeoPdf 42c 47 50 53 lower 47 63 67
49. nal letters in ASCII export files 78 C 6 Lower case international letters in ASCII export files 79 Chapter 1 Introduction 11 Why This Document This document was written as a supplement to assist students and teachers in MA206 the second year probability and statistics course required of all cadets at the United States Military Academy USMA This semester long course is the final course in the core mathematics sequence It is designed to advance the student s understanding of math ematical concepts and techniques used to model and analyze problems dealing with random effects and data 5 Because of this focus this course is not focused on the theory of probability and statistics it is focused on the application of those sciences Of course it is not possible to fruitfully apply the tools of probability and statistics or any other academic discipline without a reasonable grounding in what is actually going on But the focus of this course is on understanding of the tools applied to understanding of the real world Advanced calculators such as the HP 48 and TI 89 present both an op portunity and and a challenge to students of probability and statistics On one hand the calculator makes actually performing the sometimes tedious calculations needed in probability and statistics a matter of punching a few buttons Advanced calculators also largely or completely eliminate the need for cumbersome tables But this capability come
50. ncertainty and those estimated by other means Type B evaluation of uncertainty Type A evaluation is generally what we are deal ing with in a statistics course Type B evaluation deals with the experimenter s evaluation of other sources of error including experimental bias An extended discussion of this is beyond the scope of this document the curious ready may consult 8 In the most general case it is not true that all random variables have finite standard deviation But at this level of discussion this refinement has little consequence 31 In the development that follows we will address some of the consequences of having to estimate og Dealing with the con sequences of including non statistical estimates of uncertainty is well beyond the scope of this paper If we know the probability distribution of and the value of the para meter 0 we could compute P os 0 6 the probability that the random interval contains the true value of the pa rameter Notice that in this expression unlike most of the probability statements we have encountered the random variable is on the ends of the interval not in the center That is what the expression random interval means Further development of confidence intervals depends on what we know or can assume about the distribution of the population and the statistics we are collecting 82 Samples from a Normal Population In reality of course we do not know enough to
51. ne of the applications This functionality is described in 9 Chapter14 15 Chapter 4 Descriptive Statistics 4 1 Numerical Methods The TI 89 s one variable statistics application computes the sample mean variance and standard deviation using both the sample and popu lation formulas the median and the quartiles of the sample 4 11 Computing One Variable Sample Statistics 1 Enter the sample data into a list 2 Select the 1 1 Var Stats option from the F4 Calc menu of the Statistics with List Editor application 3 Enter the name of the list containing the sample data either by enter ing the variable name directly or by selecting 2nd VAR LINK and selecting the variable 4 Select ENTER to confirm the selection and again to compute the sta tistics Tip Theone variable statistics output includes both Sx and ox Despite the similarity of the latter label in form to the symbol 0 the population standard deviation of the random variable X 16 it is not that quantity Rather it is Nw xi x 4 1 While this statistic is sometimes useful students tend to confuse it with the sample standard deviation Xu os xy 4 2 Sy which is almost always the quantity needed from a sample cal culation Put another way if you need to calculate the standard deviation from sample data you almost certainly want Sx not OX 4 2 Graphical Methods 4 2 1 Histograms A basic histogram is on
52. nvalid input here can propogate up to the CDF hygeoPdf txt 50 START92 COMMENT NNAME hygeopdf FILE HYGEOPDF 89P hygeopdf x n succ pop 50 Func NCON ARGS x n succ pop Hypergeometric PDF MON NCON Rev 2 0 20 JUN 02 NCON D MathSci USMA Mark Wroth If n pop or succ pop Then Return Invalid parameters EndIf If max 0 n pop succ lt x and x lt min n succ Then nCr succ x nCr pop succ n x nCr pop n Else 9 EndIf NCON hypergeometric RV NCON Rev 1 1 NCON Mark Wroth EndFunc NSTOP92N o A 7 hygeocdf A 7 1 Name hygeocdf Evaluate the CDF of a hypergeometric random variable A 7 2 Description hygeocdf x n succ pop computes the probability that a hypergeo metric random variable with sample size n possible number of successes succ and population size pop assumes a value less than or equal to x The hypergeometric PMF is defined in Equation 1 the CDF is Succ Pop Succ i n i Pu 2 Pop i 0 n A 1 51 where Pop is the number of elements in the population Succ is the number of elements coded success n is the sample size Unlike the PDF there are no limits in principle on x although some care is needed to ensure that the function behaves properly at all values A 7 3 Usage This function is called directly from the Home command line the program hypergeo Section A 5 also called from the command line produces a requester to prompt the user
53. of hygeopdf to catch any parameter errors so the CDF does not need to do any independent error checking The NCO symbol represents the TI 89 comment symbol see Appen dix Ic 53 A 8 unifcdf A 8 1 Name uni fcdf Evaluate the CDF of a uniformly distributed random variable A 8 2 Description This function evaluates the CDF of a uniformly distributed random vari able defined as 0 x 0 F x E a lt x lt b A 2 1 x gt b A 8 3 Usage Inputs x The value at which the CDF is to be evaluated a The lower limit of the region for which the PDF is non zero b The upper limit of the region for which the PDF is non zero Outputs cdf Cumulative probability the probability that a uniformly distributed random variable with the specified parameters is less than or equal to x A 8 4 Example To find the probabilitity that a random variable uniformly distributed between 1 and 10 is less than 5 1 Enter unifcdf 5 1 10 in the entry line of the Home window 2 Press Enter 54 3 The expression you entered and the answer 444444 will be dis played in the History Area Note If you enter all of the parameters using exact forms the calculator will display the exact answer in this case 4 9 Entering any parameter using a decimal form the 5 in the example cause the calculator to provide the approximate answer A 8 5 TI 89 Implementation unifcdf txt 55 START92 COMMENT NNAME uni fCdf FILE UN
54. pdf Evaluate the PMF of a hypergeometric random variable A 6 2 Description hygeopdf x n succ pop computes the probability that a hypergeo metric random variable with sample size n possible number of successes succ and population size pop assumes the value x The hypergeometric PDF is defined in Equation 6 1 A 6 3 Usage Inputs x The value at which the PDF is to be evaluated n The sample size succ The total number of successes in the population 49 pop The total number of elements successes and failures in the popula tion Outputs probability The PDF value A 6 4 Example To find the probability that a random variable from a hypergeometric distribution with a population size of 50 with 15 successes and a sample size of 10 has exactly 5 successes 1 Enter hygeopdf 5 10 15 50 in the entry line of the Home window 2 Press Enter 3 The expression you entered and the answer 094903 will be dis played in the History Area Note If you enter all of the parameters using exact forms the calcula tor will display the exact answer in this case 904332 9529015 Entering any parameter using a decimal form the 5 in the ex ample cause the calculator to provide the approximate answer A 6 5 TI 89 Implementation Because of the very simple definition of hygeocdf it is important that we define hygeopdf to return zero for invalid values of x It is also appropriate to test for invalid parameter inputs an i
55. phi psi VU psi Omega Q capitalomega omega w omega Table C 2 Greek letters in ASCII export files C 3 Toolbars The Toolbar block can be used to replace the standard menu with a user defined set of menus that can actually execute blocks of code This has real potential for improving the user interface However it is not clear how to take advantage of this The principal issue is that while the custom toolbar is active it su percedes all of the other calculator functions including the home screen The following code illustrates the use of this functionality MA206CMD TXT 75 START92 COMMENT 75 N N gt STORE option Option union U Set union intersect 1 Set intersect subset C Set subset element Set element ee E EE key exponent e e italic exponential e NN i imaginary number i r radian conversion r NEN matrix transposition t xmean stat mean of x ymean stat mean of y lt lt less than or equal MEN not equal to NEN gt greater than or equal _ Z angle character diff d differential d integral f integration infinity oo infinity symbol root y radical NCON Comment symbol C unary minus o degrees symbol Table C 3 Mathematical and programming operators in ASCII export files NAME MA206CMD FILE MA206CMD 89P O Prgm C Experimenta
56. po in the discus sion of the check computations for the Equation 7 10 versus 7 11 debate Revision 14 2 2002 06 18 21 02 02 WrothMark Changed binomCI to use Devore 7 10 rather than 7 11 and midified the discussion for that program accordingly Worked some on formatting of BinomGUI to reduce the number of lines that run off the page in the printed document Since there does not appear to bea way to continue a line in the ASCII programming environment with out awkward consequences in the execution environment I have elected to add statements where needed to allow the lines to be shortened Revision 14 1 2002 06 18 19 12 46 WrothMark Added various illustrations including a cartoon from the Pointer with artist s permission Revision 14 0 16 JUN 02 MBW Converted the entire document to Nuweb and LTEX in order to take advantage of the ASCII export functions of TI Graph Link and to avoid the problems observed with missing charac ters in the HTML and RIF versions produced from the DocBook imple mentation This also allows use of the various indexing functions in the literate programming tool Nuweb and in FTX This revision puts the mechanisms in place for this but does not take full advantage of them Revision 12 20 June 2001 MBW Added chi2int discussion Revision 11 20 June 2000 MBW Additional general discussion Revision 10 19 June 2000 MBW Added an MA206 program which sets up a custom menu allowing commonly used functions to be p
57. r em eduction d Erratas lt y By Johnny Thompson Figure 2 1 A cautionary note with thanks to Cadet John Thompson USMA 04 The focus of many probability and statistics courses and many stu dents appears to be on mastering the basic computations of the subject For example a major goal during a block on the exponential random variable is being able to correctly compute probabilities involving such a random variable Facility with this calculation is then assumed later in the course With a properly set up calculator the calculation itself is simple the challenge is in knowing when to use the distribution what value to 11 use for the parameter and how to interpret the result The calculator can also largely replace the use of tables and hence of the need to standardize random variables for most purposes The exception to this is that many statistical packages including the T1 89 use and display standardized random variables in statistical tests so some understanding of the process is needed 22 Interval Probabilities Computing the probability that a random variable lies in a stated interval is a common task in the probability and statistics course Especially with the capabilities of the TI 89 there are several valid strategies students may use for computing such probabilities e Manipulate the Probability Density Function PDF or Probability Mass Function PMF directly For example integrate the PDF over
58. red Outputs The primary output of the program is the probability that the random variable lies in the closed interval a b The program also echoes the parameters entered into the program as a check on data entry error An example of the output requester that displays this information is shown in Figure A 5 4 Example A 5 5 TI 89 Implementation hypergeo txt 47 NSTART92N NCOMMENT NNAME hypergeo 47 Figure A 4 hypergeo output screen NFILE HYPERGEO 89P O Prgm NCON ARGS none Hypergeometric prob GUI NCON Rev 2 3 21 JUN 02 NCON D MathSci USMA Mark Wroth Local n succ pop a b prob usrmode getMode ALL N NusrMode setMode Exact Approx APPROXIMATE Dialog Title Hypergeometric Distn Request Sample size n Request Pop size pop Request Successes succ Request lower limit a Request upper limit b EndDlog expr n gt n expr pop gt pop expr succ gt succ expr a gt a expr b gt b NCON Check inputs NCON not implemented NCON Compute If a lt b Then Sigma ChygeoPdf x n succ pop x a b gt prob Else 48 40 gt main err PassErr EndIf NCON Display probability Dialog Title Hypergeometric Distn Text PC amp string a amp lt X lt amp string b amp amp string prob Text Text n amp string n amp N amp string pop amp M amp string succ EndDlog setMode usrMode EndPrgm STOP92 o A 6 hygeopdf A 6 1 Name hygeo
59. s above Using similar notation we define ta 2v n 1 as the value that puts probability a s outside each end of the interval giving the interval S S X Praa Xn x Laiha d 8 2 vn as a 100 1 a 2 confidence interval This is the confidence interval that the TI 89 calculates from the TInterval menu function Similarly starting from the fact that if the population is Normal with mean u and standard deviation o the random variable n 1 S 52 has a x distribution with n 1 degrees of freedom we can find that the confidence interval S 1 S n x 8 3 X pn X a 2 1 isa 100 1 a confidence interval for the variance of a Normal population This is the confidence interval computed by the Chi2int and Chi 2GUI TI 89 functions 8 3 Large Samples from Non Normal Populations If the underlying population is not Normal but has mean u and finite variance o the distribution of X is not exactly known However if the size of the sample is large the Central Limit Theorem argues that X is approximately Normal with mean u and variance 0 n Under the same assumption that the sample size is large it is reasonable to claim that S is a very precise estimate of the population variance If we assume this we know the standard deviation of X and we can use the confidence interval defined by 8 1 implemented by the TI 89 ZInterval function 35 8 4 TI 89 Functions The main TI 89 set of functions supportin
60. s of the calculator to move between different representations of the data or to make use of the Computer Algebra System CAS capabilities of the system are to be used effectively This line of research also suggests that the way the instructor presents the process of thinking about mathematics in general and probability and statistics in particular affects how students use the calculator s capabilities and how they view mathematics in general The implication of these thoughts is that instructors must become famil iar with the tools and techniques they intend their students to take away from the course and model them in the classroom Since this requires some advanced preparation both to decide how the calculator should be used and for the instructor to master the techniques involved One of the 1See for example the research summary at 10 functions of this document is to present both a point of view on this subject and to provide information allowing other instructors to reach their own conclusions The following sections are presented in an order generally conducive to a one semester course in probability and statistics following the outline of MA206 the core course in the subject taught at USMA using 4 as the text With some modification it should be helpful in most basic probability and statistics courses hat are you doing mn m putting old WPR your calculator The American taxpayers into my calculator ore paying fo
61. s with a price Not only does the student have to master the concepts of the course a challenge in itself but they must also learn what the capabilities of the calculator are and how to invoke them This document is aimed at students and teachers who are trying to master the aspects of the advanced calculator specifically the TI 89 that apply to the basic probability and statistics course It supplements the course textbook and the calculator handbook and focuses on those uses of the calculator specifically needed for this course It covers both the built in operations of the calculator and programs written specifically to assist with the subject We assume that the student has been using the same calculator through the core math sequence and is therefor familiar with basic calculator op erations In addition to basic arithmatic computation this includes sym bolic manipulation basic calculus particularly numerical quadrature and graphing of functions One of the powerful features of the advanced calculators is program mability In addition to briefly covering the built in functions of the calcula tor this document discusses some programs written to assist with subjects covered in the basic probability and statistics course and provides some additional detail on the use of functions and programs that are part of the TI 89 and TI 89 Statistics with List Editor flash application The use of the calculator functions and the implementat
62. standard uncertainty u representing the estimated standard devi ation of the measurement This is commonly written as u or in our height example 70 2 inches Another way to write this would be as the interval 6 u uc where we are treating the value of the estimator as a random variable because its value is not known in advance How should we interpret this interval The answer lies in NIST s definition of u as the standard deviation of the measurement An experimental measurement is a value computed from usually repeated observations of a quantity in our terminology a sample of all possible observations of that quantity In other words an experimental measurement is a statistic and like any other random variable it has a distribution and therefore a standard deviation So the interval we are talking about is 56 0 so Note A truly rigorous discussion would at this point have to dis cuss the consequences of the fact that while the experimenter would like to know og in reality he or she almost never does Furthermore the definition of u includes the experimenter s non statistical estimates of the uncertainty of the measurement Inclusion of these non statistical estimates makes it difficult to proceed rigorously from the standpoint of mathematical statis tics The combined standard uncertainty includes estimates of both uncertainties esti mated by statistical means Type A evaluation of u
63. stributions The TI 89 s calculus applications can significantly ease the manipulation of arbitrary continuous probability distributions through their ability to find both definite and indefinite integrals You reach these functions through the HOME screen and should already be familiar from earlier calculus courses The major caution in applying the basic calculus functions to the PDF is to ensure that the limits of integration are correctly applied Like any computer the TI 89 will do what you tell it to which may not be what you intended particularly for piecewise defined functions Probabilities Finding the probability that an arbitrarily defined continuous random vari able lies in a given interval is by definition a matter of integrating the PDF 23 over the interval For simply defined functions e g the Exponential dis tribution this is easily accomplished with the Integrate function from the HOME F3 Calc menu Expected Value Finding the expected value of an arbitrarily defined continuous random variable can be accomplished by applying the definition of expected value For simply defined functions e g the Exponential distribution this is easily accomplished with the Integrate function from the HOME F3 Calc menu For example to find the expected value of x 0 15 70150 05 des 05 fx 0 otherwise Example 4 4 we compute 0 5 amp Odx 1 0 15 e 0156705 dy oo 0 5 While this integral should be w
64. t f4 EndDlog EndIf EndPrgm STOP92 o A 12 Confidence Intervals on Variance chi2int A 12 1 Name chi2int The chi2int O program and its companion chi2gui O which provides a graphical user interface to the program computes confidence intervals on the population variance or standard deviation 64 A 12 2 Usage Inputs This function can be called in either of two ways from the Home com mand line as chi2int n s2 clevel type or by calling chi2gui O If the chi2int for is used the input arguments are n The number of samples in the sample s2 The sample variance clevel The desired confidence level for the confidence interval type The type of interval desired where 1 indicates a confidence interval onthe variance and 2 a confidence interval on the standard deviation If the chi2guiO form is used there are no command line inputs the program will raise a requester to allow the user to supply the needed values Outputs The chi2int program provides its outputs in two forms a graphical re quester that provides the requested confidence interval and echoes the user inputs and by storing the user inputs and the desired confidence interval endpoints in the statvars directory The set of stored variables are different for the chi2int and the chi2gui programs The chi2int stores statvars lower The lower end of the desired confidence interval statvars upper The upper end of the desired confidence interval In
65. te that some symbols are not the same as the obvious key symbol This specificially includes the exponential symbol and the negation operator which is not the same as the subtraction operator ASCII Calculator Meaning NCON O Comment lambda A Greek letter mu u Greek letter sigma o Greek letter gt Store command Sigma by Summation command root y Square root command e e Exponential NON Negation lt lt Math symbol gt gt Math symbol Table C 1 Control sequences in ASCII export files Tables C 2 through C 6 are an expanded version of the Table C 1 based on 13 The general format of the ASCII program files is a header of the form NSTART92N COMMENT NAME NormCDF FILE NORMCDF 89P 74 where the strings NormCDF and NORMCDE 89P are replaced by the appropriate names This is followed by the argument list in parentheses following which is either a Prgm EndPrgm block or a Func EndFunc block These blocks contain the appropriate program code Finally the program ends with a trailer of the form NSTOP92N alpha a alpha beta p beta Gamma DL capital gamma gamma y gamma Delta A capital delta delta 6 delta epsilon epsilon zeta C zeta theta 0 theta lambda A lambda xi xi Pi II capital pi pi m pi mu u mu rho p tho Sigma X capital sigma sigma O sigma NtauN T tau phi
66. ted to the computer itself This document is a literate program in the sense that the program listings found in this document are copied to disk as part of processing this docu ment with Nuweb 2 The resulting text files can then be imported into Graph Link and ultimately downloaded to the calculator In this manner the version of the program displayed here is kept current with the version actually loaded on the calculator Using this system is discussed in Appendix B with regard to creating the actual calculator files and in Appendix F with regard to producing the documentation C 2 ASCII Format for TI 89 Programs Because of the desire to record the programs in this document and the literate programming orientation of it the calculator programs shown here are in the ASCII export format of the TI GraphLink software The format of an ASCII text file for a TI 89 program is as far as I can see undocumented This makes editing the programs something of a 73 challenge In general while I use the ASCII storage form for inclusion in this document most program development is done in the Graph Link editor However some observations can be made about the ASCII export format e The backslash character V appears to serve as an escape character preceding and following special characters and preceding certain keywords at the beginning of the file e Certain specific characters appear to be as shown in Table C 1 e No
67. the TI 89 uses we take a simple test case Since the approximation given by Equation A 5 will improve with larger n we will choose as our test case n 2 and number of successes 1 With this assumption f 4 0 5 Selecting a 0 5 and hence Za 2 0 67449 we have now determined the values we need to use for our calculations Using Matlab as a calculator the lower limit calculated with Equa tion A 4 is 0 28475881963799 The equivalent value for Equation eqn 7 11 is 0 26153177357874 Applying the 1 Proportion Z Interval function of the TI 89 with Success 1 n 2 and CI 0 5 the calculator returns a confidence interval of 0 2615 0 7385 Since Eon ES would have returned at that level of precision 0 2753 and Equation would have returned 0 2615 we can conclude that the calculator uses Equation A 5 or something very similar to it A 11 3 Usage There are three different ways to access this basic functionality e Select the TI 89 Statistics with List Editor F7 Ints menu item 5 1 PropZInt and fill in the required values Outputs are displayed in a dialog box and stored in the StatVars directory e Enter at the command line TIStat Zint 1P x n clev Outputs are stored in the StatVars directory but not displayed e Enter at the command line ma206 binomCI O and fill in the required values in the resulting dialog box Outputs are displayed in a dialog box and stored in the StatVars directory Both all three methods take by
68. tial Distn Request Lower bound lo Request Upper bound hi Request lambda NlambdaN EndDlog If ok 1 Then expr lo gt lo expr hi gt hi expr lambda gt lambda ExpCDF hi lambda ExpCDF lo lambda gt cdf Dialog Title Exponential Distn Text P amp string lo amp lt X lt amp string hi amp amp format cdf 4 Text 58 Text lambda amp string lambda EndDlog setMode usrMode EndIf EndPrgm STOP92 o A 11 Confidence Intervals on the Binomial Pro portion A 11 1 Name TIStat zInt_1P x n clevel compute confidence interval on the population proportion for a binomial distribution BinomCI Calculate and store a confidence interval on the popula tion proportion for a binomial distribution using 4 Equation 7 10 A 11 2 Discussion There are two different formulas for a confidence interval on a population proportion given by Devore in equations 7 10 and 7 11 The TI 89 computes a confidence interval for the population but the documentation does not specify which formula it uses The two formule are P 22 zap B e AA 1 2 aim valid for all land P z3 Vpqin A 5 valid when np gt 10 and ng gt 10 Devore citing I indicates that this expression gives a more accuract confidence interval than Equation A 5 and the side conditions need not be checked for this form 59 To determine which equation
69. tion of a binomial distribution However this function appears to use the approximate formula defined by Devore p 291 in Equation 7 11 which is the standard form used by most texts rather than the more exact form defined in Equation 7 10 There do not appear to be direct functions for the calculation of x con fidence intervals on variance The F5 Distr menu s2 Inverse sub menu does include an Inverse Chi square function which can be used to provide the Chi squared critical values needed to compute the confidence intervals however The chi2gui calculator program is designed to fill this lack and functions in a manner similar to the built in TI 89 programs 36 Chapter 9 Hypothesis Testing The F6 Tests menu includes applications for among others Z and T based hypothesis tests These tests allow the test statistic to be provided or to be computed from data entered in one of the lists In all cases the calculator provides the p value relevant to the test rather than drawing a conclusion 37 Appendix A Program and Function Reference This Appendix provides use information for selected TI 89 programs in cluding functions provided with the calculator those belonging to the Statistics with List Editor application and those provided in calculator pro grams defined in this document Implementation details are provided for functions and programs de fined by this document This includes a complete listing of the calculator
70. tistics X The sample mean Y x The sample total Y x The sum of the squared observations Sx The sample standard deviation computed as aou c n 1 The population standard deviation computed as Lae xy n Note that this is the the true population standard deviation only if the entire population is part of the list on which the statistics are computed This value is not the population standard deviation for any other sample A common mistake made by students is to use this value for an unknown population standard deviation 28 n The sample size Min The sample minimum Q1 The first sample quartile the value below which one quarter of the sample observations fall Med The sample median the value below which half of the sample ob servations fall Q3 The third sample quartile the value below which three quarters of the sample observations fall Max The sample maximum Y x x Sum of the squared deviations The interval estimation functions provided by the TI 89 will also pro vide the point estimates of the relevant parameter when they compute the value based on a list containing the sample data 29 Chapter 8 Confidence Intervals The following development more theoretical and expository than the rest of this document is intended to provide an alternate intro duction to confidence intervals more directly tied to the capabilities introduced by the advanced calculator than the equivalent mat
71. try reloads the custom menu primarily for use in debugging MA206 TXT 40b 40 Title Tools Item NewProb Item MA206 Item CustmOff Item autoaoffQ Item uninevhk Q o File defined by 40ab 41ab 42abc The last two menu items are useful only if you have installed the autoaoff assembly program See Section C 4 3 for discussion of this program The uninevhk for uninstall event hook function is part of the same package and uninstalls autoaoff restoring the default behavior of the calculator The Calc menu provides easy access to functions commonly needed in calculations MA206 TXT 4la Title Calc Item integral C Item ASigmaN Item root C o File defined by 40ab 41ab 42abc The Counting menu provides access to several functions used specifically in counting problems All of these functions are built in to the TI 89 this menu just makes accessing them convenient MA206 TXT 41b Title Counting Item nPr Item nCr Item o File defined by 40ab 41ab 42abc The Distr menu provides command line access to several functions related to computing probabilities directly from the command line 41 MA206 TXT 42a Title Distr Item ma206 binomGUIQ Item TIStat PoissPdf Item TIStat PoissCdf Item ma206 hypergeo Item ma206 expGUIQ Item ma206 unifGUI Item ma206 NormCDF o File defined by 40ab 41ab 42abc The Distr menu provides command line
72. u items It can also be accessed through the binomGUI program described later in this document Section A 4 describes the use and implementation of this function 6 13 Hypergeometric Distribution The Hypergeometric probability distribution is not one of the pre defined distributions in the Statistics with List Editor Since it is not pre defined for us we can define the PDF and CDF as TI 89 functions hypergeo Section A 5 is a program interface to those functions The PDF of the hypergeometric distribution is shown in Succ Pop Succ x Heu pax m 6 1 n Where Pop is the number of elements in the population 22 Succ is the number of elements coded success n is the sample size and max 0 n Pop Succ x min n Succ 6 2 The side conditions deal with the fact that the minimum number of successes in the sample is limited by the total number of failures in the population and the sample size you can t have more failures in the sample than there are in the population and the maximum number of successes in the sample is limited by the number of successes in the population 6 1 4 Poisson Distribution The Poisson probability distribution is one of the pre defined probability distribution in the Statistics with List Editor application It is accessed via the F5 Distr menu using either the D Poisson Pdf or E Poisson Cdf menu items 6 2 Continuous Random Variables 6 2 1 Arbitrary Di
73. ud upside down exclamation ud upside down question mark MAIN capital A grave A capital A acute MAN capital A circumflex MAN capital A tilde A capital A dieresis Ao capital A ring AE capital AE c capital C cedilla E capital E grave AEP capital E acute E capital E circumflex E capital E dieresis I capital I grave AAN capital I acute NIN capital I circumflex I capital I dieresis D capital D bar NN capital N tilde NON capital O grave NO N capital O acute NO N capital O circumflex NON capital O tilde NO N capital O dieresis x times x mark 0 capital O slash U capital U grave U capital U acute U capital U circumflex U capital U dieresis ANA capital Y acute I gt capital I p Table C 5 Upper case international letters in ASCII export files 78 ss eschett a a grave a a acute a a circumflex a a tilde a a dieresis ao a ring ae ae c c cedilla Ng e grave e e acute Ne N e circumflex e e dieresis NEON i grave MUN i acute MN i circumflex MA i dieresis NON d bar NA n tilde NON o grave o O acute NO N o circumflex o o tilde o o dieresis WA division symbol o o slash NUN u grave u u acute NN u circumflex u u dieresis NEN y acute i gt ip MN y dieresis Table C 6 Lower case international letters in ASCII export files 79 Goto st

TI-89 in MA206 - West-Point.ORG, The West Point Connection

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