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Texas Instruments TI-86 Manual Book

Inferential statistics and distribution functions
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See also: Setup Manual , Manual Book
TI-86 Inferential Statistics and
Distribution Functions
Installing the Inferential Statistics and Distribution Features for Use ................................................. 2
Displaying the STAT (Inferential Statistics and Distribution) Menu..................................................... 3
The STAT Menu................................................................................................................................... 3
Uninstalling the Inferential Statistics and Distribution Features ......................................................... 3
Example: Mean Height of a Population ......................................................... 4
Interpreting the Results ...................................................................................................................... 5
Inferential Statistics Editors ........................................................................... 7
Displaying the Inferential Statistics Editors......................................................................................... 7
Using an Inferential Statistics Editor................................................................................................... 7
Bypassing the Inferential Statistics Editors ......................................................................................... 8
STAT TESTS (Inferential Statistics Tests) Menu ................................................................................... 9
Test and Interval Output Variables .............................................................. 26
Distribution (DISTR) Functions ...................................................................... 28
STAT DISTR (Inferential Statistics Distribution) Menu....................................................................... 28
DRAW (Distribution Shading) Functions ...................................................... 33
STAT DRAW (Inferential Statistics Draw) Menu................................................................................ 33
FUNC (Function) Parameters ......................................................................... 35
STAT FUNC (Inferential Statistics Functions) Menu .......................................................................... 35
MATH menu (where STAT is automatically placed) .......................................................................... 39
(MATH) STAT (Inferential Statistics and Distribution) Menu ............................................................. 39
STAT TESTS (Inferential Statistics Tests) Menu ................................................................................. 39
STAT DISTR (Inferential Statistics Distribution) Menu....................................................................... 39
STAT DRAW (Inferential Statistics Draw) Menu................................................................................ 39
STAT FUNC (Inferential Statistics Functions) Menu .......................................................................... 39

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  • Page 1: Table Of Contents

    Loading and Installing Inferential Statistics and Distribution Features on Your TI-86 ............... 2 Loading the Inferential Statistics and Distribution Features into TI-86 Memory......... 2 Installing the Inferential Statistics and Distribution Features for Use ..........2 Displaying the STAT (Inferential Statistics and Distribution) Menu............. 3 The STAT Menu...........................

  • Page 2: Loading And Installing Inferential Statistics And Distribution Features On Your Ti-86

    To load the inferential statistics and distribution features onto your TI-86, you need a computer and the TI-86 Graph Link software and cable. You also need to download the statistics program file from the Internet and save it on your computer.

  • Page 3: Displaying The Stat (Inferential Statistics And Distribution) Menu

    Display the home screen. Displaying the STAT (Inferential Statistics and Distribution) Menu - Π/ If other assembly language When you install the inferential statistics and distribution program on your TI-86 programs are installed, STAT and activate it, becomes the last item on the menu.

  • Page 4: Deleting The Inferential Statistics And Distribution Program From Ti-86 Memory

    Assembly Language Programming: Inferential Statistics and Distribution Functions Deleting the Inferential Statistics and Distribution Program from TI-86 Memory Deleting the program does - ™ ' Select DELET from the not delete the variables menu. associated with the program. Select PRGM...

  • Page 5: Interpreting The Results

    Assembly Language Programming: Inferential Statistics and Distribution Functions Ë Í Enter the first height value. As you enter it, it is displayed on the bottom line. The value is displayed in the first row, and the rectangular cursor moves to the next row. Enter the other nine height values the same way.
  • Page 6 Assembly Language Programming: Inferential Statistics and Distribution Functions : - Œ Display the inferential statistics / ' & / and distribution editor for TIntl ( ~ Í and select Stats in the Inpt field. Enter the test requirements: Store 64.5 to þ ¦...

  • Page 7: Inferential Statistics Editors

    Assembly Language Programming: Inferential Statistics and Distribution Functions The parameters are y ¡ ¢ The answer ( 69.1121340648) ShdNm( lowerbound, ¢ ¢ Ë from step 14 is the lower bound. upperbound [ , m, s ]) . ¤ 1å99 is the upper bound. The normal curve is defined by a mean of 65 and a standard...

  • Page 8: Bypassing The Inferential Statistics Editors

    Assembly Language Programming: Inferential Statistics and Distribution Functions Select No or Yes for the & or ' Select Calc Draw (when Draw Pooled option, if the selection is available) to execute the is available. The Pooled instruction. option is available for Tsam2 and TInt2 only.

  • Page 9: Inferential Statistics Editors For The Stat Tests Instructions

    Assembly Language Programming: Inferential Statistics and Distribution Functions Inferential Statistics Editors for the STAT TESTS Instructions - Π/ ' & STAT TESTS (Inferential Statistics Tests) Menu TESTS DISTR DRAW FUNC Uninst RsltOn RsltOf ZTest TTest Zsam2 Tsam2 ZPrp1 ZPrp2 ZIntl TIntl ZInt2...
  • Page 10 Assembly Language Programming: Inferential Statistics and Distribution Functions All examples on pages 10 through 23 assume a fixed-decimal mode setting of four. If you set the decimal mode to or a different fixed-decimal setting, your Float output may differ from the output in the examples. Be sure to turn off the y= functions before drawing results.
  • Page 11 Assembly Language Programming: Inferential Statistics and Distribution Functions TTest This one-sample t-test, shown as in the editor, performs a hypothesis test T-Test for a single unknown population mean m when the population standard deviation s is unknown. It tests the null hypothesis H : m=m against one of the alternatives below.
  • Page 12 Assembly Language Programming: Inferential Statistics and Distribution Functions Zsam2 This two-sample Z-test, shown as in the editor, tests the equality of 2-SampZTest and m the means of two populations (m ) based on independent samples when and s both population standard deviations (s ) are known.
  • Page 13 Assembly Language Programming: Inferential Statistics and Distribution Functions Tsam2 This two-sample t-test, shown as in the editor, tests the equality of the 2-SampTTest and m means of two populations (m ) based on independent samples when or s neither population standard deviation (s ) is known.
  • Page 14 Assembly Language Programming: Inferential Statistics and Distribution Functions ZPrp1 This one-proportion Z-test, shown as in the editor, computes a test for 1-PropZTest an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. ZPrp1 tests the null hypothesis H : prop=p...
  • Page 15 Assembly Language Programming: Inferential Statistics and Distribution Functions ZPrp2 This two-proportion Z-test, shown as in the editor, computes a test to 2-PropZTest compare the proportion of successes (p1 and p2) from two populations. It takes as input the count of successes in each sample (x1 and x2) and the count of observations in each sample (n1 and n2).
  • Page 16 Assembly Language Programming: Inferential Statistics and Distribution Functions ZIntl This one-sample Z confidence interval, shown as in the editor, computes a ZInterval confidence interval for an unknown population mean m when the population standard deviation s is known. The computed confidence interval depends on the user-specified confidence level.
  • Page 17 Assembly Language Programming: Inferential Statistics and Distribution Functions ZInt2 This two-sample Z confidence interval, shown as in the editor, 2-SampZInt computes a confidence interval for the difference between two population means ) when both population standard deviations ( s and s ) are known.
  • Page 18 Assembly Language Programming: Inferential Statistics and Distribution Functions TInt2 This two-sample t confidence interval, shown as in the editor, 2-SampTInt computes a confidence interval for the difference between two population means ) when both population standard deviations ( s and s ) are unknown.
  • Page 19 Assembly Language Programming: Inferential Statistics and Distribution Functions ZPin1 This one-proportion Z confidence interval, shown as in the editor, 1-PropZInt computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample x and the count of observations in the sample n.
  • Page 20 Assembly Language Programming: Inferential Statistics and Distribution Functions Chitst This test, shown as in the editor, computes a chi-square test for Test association on the two-way table of counts in the matrix you specify at the prompt. The null hypothesis H for a two-way table is: no association Observed exists between row variables and column variables.
  • Page 21 Assembly Language Programming: Inferential Statistics and Distribution Functions ÜSam2 This two-sample Û-test, shown as in the editor, computes an Û-test to 2-SampÜTest and s compare two normal population standard deviations (s ). The population Ü Ü Sam2 means and standard deviations are all unknown. , which uses the ratio of sample variances Sx1 /Sx2...
  • Page 22 Assembly Language Programming: Inferential Statistics and Distribution Functions TLinR This linear regression t-test, shown as in the editor, computes a linear LinRegTTest regression on the given data and a t-test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H : b=0 (equivalently, r =0) against one of the alternatives below.
  • Page 23 Assembly Language Programming: Inferential Statistics and Distribution Functions ANOVA This test computes a one-way analysis of variance for comparing the means of 2 to 20 populations. The ANOVA procedure for comparing these means involves analysis of the variation in the sample data. The null hypothesis H =...=m :.

  • Page 24: Inferential Statistics And Distribution Input Descriptions

    Assembly Language Programming: Inferential Statistics and Distribution Functions Inferential Statistics and Distribution Input Descriptions This table describes the inferential statistics and distribution inputs. You enter values for these inputs in the inferential statistics editors. The table presents the inputs in the same order as they appear in the editor examples on pages 10-23. Input Description Hypothesized value of the population mean that you are testing.
  • Page 25 Assembly Language Programming: Inferential Statistics and Distribution Functions Input Description The matrix name that represents the columns and rows for the Observed (Matrix) observed values of a two-way table of counts for the Chitst must contain all integers ‚ 0. Matrix dimensions must be Observed at least 2×2.

  • Page 26: Test And Interval Output Variables

    If you upload TI-86 variables that contain the sigma (s) or mu (m) symbols to your computer, the Graph Link program will prompt you to rename them. This is because computer file names cannot contain these symbols. When you download the renamed variables to your TI-86, Graph Link restores the symbols and the files are loaded in the calculator under their original names.
  • Page 27 Assembly Language Programming: Inferential Statistics and Distribution Functions TI-86 Variables Variables and TLinR, Math Catalog / Variables Menu Tests Intervals ANOVA Symbols number of data points REAL standard error about the line REAL regression/fit coefficients a, b a, b STAT...

  • Page 28: Distribution (Distr) Functions

    Assembly Language Programming: Inferential Statistics and Distribution Functions Distribution (DISTR) Functions - Π/ ' ' STAT DISTR (Inferential Statistics Distribution) Menu TESTS DISTR DRAW FUNC Uninst RsltOn RsltOf nmpdf nmcdf invnm tpdf tcdf chipdf chicdf Fpdf Fcdf bipdf bicdf pspdf pscdf gepdf...
  • Page 29 Assembly Language Programming: Inferential Statistics and Distribution Functions nmcdf Computes the normal distribution probability between lowerbound and upperbound for the specified mean m and standard deviation s . The defaults are m =0 and s =1. lowerbound upperbound[ nmcdf( invnm Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean m and standard deviation s .
  • Page 30 Assembly Language Programming: Inferential Statistics and Distribution Functions chipdf Computes the probability density function (pdf) for the c (chi-square) distribution at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c distribution, paste to the y= editor.
  • Page 31 Assembly Language Programming: Inferential Statistics and Distribution Functions Ü Ü Computes the Û distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. numerator df and denominator df must be integers > 0. Ü...
  • Page 32 Assembly Language Programming: Inferential Statistics and Distribution Functions pscdf Computes a cumulative probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be a real number or a list of real numbers.

  • Page 33: Draw (Distribution Shading) Functions

    Assembly Language Programming: Inferential Statistics and Distribution Functions DRAW (Distribution Shading) Functions - Π/ ' ( STAT DRAW (Inferential Statistics Draw) Menu TESTS DISTR DRAW FUNC Uninst RsltOn RsltOf ShdN Shdt ShdChi ShdF Instruction Function ShdN Shades normal distribution Shades Student-t distribution Shdt Shades c...
  • Page 34 Assembly Language Programming: Inferential Statistics and Distribution Functions ShdChi Draws the density function for the c (chi-square) distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. lowerbound upperbound ShdChi( Note: For this example, xMin = 0 xMax = 35 xScl = 1 yMin = L.025...

  • Page 35: Func (Function) Parameters

    Assembly Language Programming: Inferential Statistics and Distribution Functions FUNC (Function) Parameters - Π/ ' ) STAT FUNC (Inferential Statistics Functions) Menu TESTS DISTR DRAW FUNC Uninst RsltOn RsltOf Ztest TTest ZSam2 Tsam2 ZPrp1 ZPrp2 ZIntl TIntl ZInt2 TInt2 ZPIn1 ZPIn2 Chitst FSam2...
  • Page 36 Assembly Language Programming: Inferential Statistics and Distribution Functions Function Argument and Result list1 list2 list3 list20] ANOVA( Performs a one-way analysis of variance for comparing the means of 2 to 20 populations. observedmatrix expectedmatrix[ drawflag] Chitst( Performs a chi-square test. drawflag= draws results;...
  • Page 37 Assembly Language Programming: Inferential Statistics and Distribution Functions Function Argument and Result alternative pooled drawflag] Tsam2 where v 1 n2 refers to summary statistics that you must enter. is ƒ ; Computes a two-sample t-test. alternative= is < ; alternative= alternative= is >.
  • Page 38 Assembly Language Programming: Inferential Statistics and Distribution Functions Function Argument and Result listname1 listname2[ freqlist1 freqlist2 alternative drawflag] ZSam2( where s listname1 listname2 refers to the known population standard deviations (from the first and second populations) and lists you have created in the list editor.

  • Page 39: Menu Map For Inferential Statistics And Distribution Functions

    Assembly Language Programming: Inferential Statistics and Distribution Functions Menu Map for Inferential Statistics and Distribution Functions - ΠMATH menu (where STAT is automatically placed) PROB ANGLE MISC INTER STAT - Π/ ' (MATH) STAT (Inferential Statistics and Distribution) Menu TESTS DISTR DRAW...

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