Texas instruments TI-86 Inferential Statistics and Distribution Functions

TI-86 Inferential Statistics and

Distribution Functions

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................................................................................................................................... 3

Uninstalling the Inferential Statistics and Distribution Features.........................................................3

Deleting the Inferential Statistics and Distribution Program from TI-86 Memory...............................4

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

Inferential Statistics Editors for the STAT TESTS Instructions ....................9

STAT TESTS (Inferential Statistics Tests) Menu...................................................................................9

Inferential Statistics and Distribution Input Descriptions.........................24

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

Menu Map for Inferential Statistics and Distribution Functions .............. 39

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

Assembly Language Programming: Inferential Statistics and Distribution Functions

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.

Loading the Inferential Statistics and Distribution Features into TI-86 Memory

When sending a program from your computer to the TI-86, the calculator must no be in Receive mode. The Receive mode is used when sending programs or data from one calculator to another.

Start the TI-86 Graph Link on your computer.

Turn on your TI-86 and display the home screen.

Click on the Send button on the TI-86 Graph Link toolbar to display the Send dialog box.

WLink86.exe

- l

Other files associated with the assembly language program (

statedit

PRGM NAMES

need not do anything with them.

For assembly language programs that must be installed, up to three can be installed at a time (although the TI-86 can store as many as permitted by memory). To install a fourth, you must first uninstall (page 3) one of the others.

exstats, exstats2

) appear on the

menu, but you

Specify the statistics program file as the file you want to send.

Send the program to the TI-86. The program and its associated executable file become items on

PRGM NAMES

the

Exit Graph Link.

menu.

infstat1.86g

Installing the Inferential Statistics and Distribution Features for Use

Use the assembly language program

Infstats

to install the inferential statistics and distribution features directly into the TI-86’s built-in functions and menus. After installation, the inferential statistics and distribution features are available each time you turn on the calculator. You do not need to reinstall them each time. When you run assembly language programs that do not install themselves into the

- Œ / menu, their features are lost when you turn off the calculator.

All examples assume that on your TI-86. The position of

Infstats

STAT

is the only assembly language program installed

on the

MATH

menu may vary, depending on

how many other assembly language programs are installed.

Asm(

Select to paste it to a blank line on the home screen.

Select

NAMES

to the home screen as an argument.

from the

Infstat

from the

menu to paste

CATALOG

PRGM

Infstats

- w & #

(move 4 to

Asm(

)

8 &

Infstat

(select

Assembly Language Programming: Inferential Statistics and Distribution Functions

The variables that will be overwritten are listed on page 26.

If other assembly language programs are installed, may be in a menu cell other

- Œ / '

than

STAT

Run the installation program.

Caution:

If you have values

stored to variables used by the statistical features, they will be overwritten. To save your values, press * to exit, store them to different variables, and then repeat this installation.

Continue the installation. Your

version number may differ from the one shown in the example.

Display the home screen.

Displaying the STAT (Inferential Statistics and Distribution) Menu - Œ /

When you install the inferential statistics and distribution program on your TI-86 and activate it,

NUM PROB ANGLE HYP MISC 4 INTER STAT

STAT

becomes the last item on the

Inferential Statistics and Distribution Menu

MATH

menu.

When you uninstall the inferential statistics and distribution features, the statistics assembly language programs (

exstats2,

remain in memory, but the

STAT

the

Infstats, exstats,

statedit

and

option is removed from

MATH

menu.

)

The STAT Menu - Œ / '

TESTS DISTR DRAW FUNC Uninst 4 RsltOn RsltOf

Inferential Distribution Uninstall Results Off Statistics Shading Instruction (Default) Test Editors

Functions Statistics (Intermediate calculation

Distribution Inferential Results On

Test Functions results display)

Uninstalling the Inferential Statistics and Distribution Features

Display the then select

If you are sure you want to uninstall, select confirmation menu. The menu is removed and the home screen is displayed. Your version number may differ from the one shown in the example.

STAT

Uninst

menu, and

Yes

from the

- Œ / ' *

)

STAT

Assembly Language Programming: Inferential Statistics and Distribution Functions

Deleting the Inferential Statistics and Distribution Program from TI-86 Memory

Deleting the program does not delete the variables associated with the program.

Select menu.

Select

DELET

PRGM

menu.

from the

MEM

- ™ '

/ *

Move the selection cursor to

Infstats

Move the selection cursor to

exstats

down and delete

statedit

Display the home screen.

, and then delete it.

and then delete it. Scroll

exstats2

and

(as needed)

Example: Mean Height of a Population

Estimate the mean height of a population of women, given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean. The 10 height values below are the first 10 of 90 values, randomly generated from a normally distributed population with an assumed mean of 65 inches and a standard deviation of 2.5 inches.

This example uses an inferential statistics editor. An editor prompts you for test information. See page 7 for another example of using an inferential statistics editor. You can also enter test parameters without using an editor. See page 8 for an example of bypassing the inferential statistics editors.

Height (in Inches) of Each of 10 Women

66.7 66.3 62.8 66.9 62.9 71.4 67.4 63.8 65.8 62.8

Create a new list column. The cursor indicates that alpha-lock is on. The existing list name columns shift to the right.

Note:

Your statistics editor may not look like the one pictured here, depending on the lists you have already stored.

Enter the list name at the prompt. The list to which you will store the women’s height data is created.

Move the cursor onto the first row of the list. displayed on the bottom line.

HGHT(1)=

Name=

- š ' }

y p

[H] [G] [H] [T]

†

Assembly Language Programming: Inferential Statistics and Distribution Functions

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.

Display the inferential statistics

TInterval

editor for the

Select

Enter the test requirements:

Calculate are displayed on the home screen.

Note:

the screen.

TIntl

(

STAT TESTS

Data

Set alpha-lock and enter the

List

name.

Enter 1 at the

Enter a 99 percent confidence level at the

C-Level=

Press .,

to clear the results from

menu.

Inpt

in the

Freq=

prompt.

the test. The results

. - Œ

) from

field. If

prompt.

, or

/ ' & / (

press |

† 1 1

[H] [G] [H] [T]

†

† Ë

Stats

is selected,

Interpreting the Results

The first line

(62.887,68.473)

shows that the 99 percent confidence interval for the population mean is between about 62.9 inches (5 feet 2.9 inches) and 68.5 inches (5 feet 8.5 inches). This is about a 5.6-inch spread.

The .99 confidence level indicates that in a very large number of samples, we expect 99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 65 inches, which is in the calculated interval.

The second line gives the mean height of the sample þ used to compute this interval. The third line gives the sample standard deviation gives the sample size

. The bottom line

To obtain a more precise bound on the population mean m of women’s heights, increase the sample size to 90. Use a sample mean þ of 64.5 and sample standard deviation

Stats

(summary statistics) input option.

of 2.8 calculated from the larger random sample. This time, use the

Assembly Language Programming: Inferential Statistics and Distribution Functions

The parameters are

invnm(

area[, m, s

]).

Display the inferential statistics and distribution editor for and select

Enter the test requirements:

Store 64.5 to

Store 2.8 to

Store 90 to

Calculate the test. The

Stats

in the

Inpt

results

TIntl

field.

: - Œ / ' & / ( ~ Í

Ë 5

†

Ë 8

are displayed on the home screen.

If the height distribution among a population of women is normally distributed with a mean

of 65 inches and a standard deviation σ of 2.5 inches, what height is

exceeded by only 5 percent of the women (the 95th percentile)?

invnm(

invnm

STAT DISTR

to the home

stands for

‘ y Œ

/ ' '

(

Display the (Distributions) menu.

Paste screen. ( Inverse Normal.)

Enter .95 as the area, 65 as µ, and 2.5 as σ.

The result is displayed on the home screen; it shows that five percent of the women are taller than 69.1 inches (5 feet 9.1 inches).

Now graph and shade the top five percent of the population.

Set the window variables to these values:

xMin=55 yMin=L.05 xRes=1 xMax=75 yMax=.2 xScl=2.5 yScl=0

Display the

Paste screen. (

STAT DRAW

ShdNm(

ShdNm

to the home

stands for Shade

Normal.)

menu.

6 '

. y Œ / ' (

Assembly Language Programming: Inferential Statistics and Distribution Functions

The parameters are

ShdNm(

upperbound

lowerbound,

, m, s

[

The answer (

)

]

from step 14 is the lower bound. 1å99 is the upper bound. The

Ans

69.1121340648)

y ¡ ¢

¢ 65 ¢ 2 Ë

normal curve is defined by a mean µ of 65 and a standard deviation σ of 2.5.

Plot and shade the normal curve.

Area=

is the area above the 95th percentile. bound.

low=

is the lower

up=

is the upper bound.

You can remove the menu from the bottom of the screen.

Inferential Statistics Editors

Displaying the Inferential Statistics Editors

When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary according to each test or interval’s input requirements.

When you select the

ANOVA(

instruction, it is pasted to the home screen.

does not have an editor screen.

ANOVA(

Data

Select lists as input. Select enter summary statistics, such as v, Sx, and n as inputs.

Most of the inferential statistics editors for the hypothesis tests prompt you to select one of three alternative hypotheses.

to enter the data

Stats

Using an Inferential Statistics Editor

This example uses the inferential statistics editor for

Select a hypothesis test or confidence interval from the

STAT TESTS

menu. The

appropriate editor displays.

Select

Data

Stats

input, if the

selection is available.

Enter real numbers, list names, or expressions for each argument in the editor. See the input descriptions table on page 24.

Select the alternative hypothesis against which to test, if the selection is available.

- Œ / ' & '

(displays

TTest

the

[H] [G] [H] [T]

or !

editor)

TTest

Assembly Language Programming: Inferential Statistics and Distribution Functions

Select No or Pooled option, if the selection is available. The Pooled option is available for

TInt2

and

! b

¦ Select

want the variances pooled. Population variances can be unequal.

¦ Select

variances pooled. Population variances are assumed to be equal.

Yes

for the

only. Press " or

to select an option.

if you do not

Yes

if you want the

Tsam2

Select

Calc

Draw

(when Draw

is available) to execute the instruction.

When you select results are displayed on the

Calc

, the

home screen.

When you select

Draw

, the

results are displayed in a graph (not available for a confidence interval).

Bypassing the Inferential Statistics Editors

You can paste a hypothesis test or confidence interval instruction to the home screen without displaying the corresponding inferential statistics editor. You can also paste a hypothesis test or confidence interval instruction to a command line in a program.

RsltOn

Turn

Note:

The default is

(Results Off).

(Results On).

RsltOf

- Œ / ' / & b

This example uses summary statistics. See pages 35-38 for a list of menu parameters.

FUNC

(Function)

Select the instruction from the

STAT FUNC

Input the syntax for each

menu.

hypothesis test and confidence interval instruction. Complete the syntax by using one of the options below:

Enter 0 (zero) as the last parameter to display the results on the home screen.

Note:

The home screen does

not display the results if you

RsltOf

use

– or –

Enter 1 as the last parameter to display the results in a graph. The graph is drawn whether you use

RsltOf

RsltOn

: / ) '

(for the

TTest

instruction)

65 P 65.68

2.71735165188 0

E b

You can remove the menu from the bottom of the screen.

Assembly Language Programming: Inferential Statistics and Distribution Functions

Inferential Statistics Editors for the STAT TESTS Instructions

STAT TESTS (Inferential Statistics Tests) Menu - Œ / ' &

TESTS DISTR DRAW FUNC Uninst

ZTest TTest Zsam2 Tsam2 ZPrp1

RsltOn RsltOf

ZPrp2 ZIntl TIntl ZInt2 TInt2

ZPin1 ZPin2 Chitst FSam2 TLinR

ANOVA

Test Name Description Function

ZTest TTest Zsam2 Tsam2 ZPrp1 ZPrp2 ZIntl

TIntl

ZInt2

TInt2

ZPin1

ZPin2

Chitst FSam2 TLinR ANOVA

One-sample Z-test Test for one m , known

One-sample t-test Test for one m, unknown

Two-sample Z-test Test comparing two m’s, known s’s

Two-sample t-test Test comparing two m’s, unknown s’s

One-proportion Z-test Test for one proportion

Two- proportion Z-test Test comparing two proportions

One-sample Z confidence interval Confidence interval for one m,

known

One-sample t confidence interval Confidence interval for one m,

unknown

Two-sample Z confidence interval

Two-sample t confidence interval Confidence interval for difference of

One-proportion Z confidence interval

Two-proportion Z confidence interval

Chi-square test Chi-square test for two-way tables

Two-sample Û-test Test comparing two s’s

Linear regression t-test t-test for regression slope and

One-way analysis of variance One-way analysis of variance

Confidence interval for difference of two m’s, known s’s

two m’s, unknown s’s

Confidence interval for one proportion

Confidence interval for difference of two proportions

This section provides a description of each

STAT TESTS

instruction and shows the

unique inferential statistics editor for that instruction with example arguments.

Descriptions of instructions that offer the

Data/Stats

input choice show both

types of input screens. Descriptions of instructions that do not offer the

Data/Stats

input choice show

only one input screen.

The description then shows the unique output screen for that instruction with the example results.

Descriptions of instructions that offer the

Calculate/Draw

output choice show

both types of screens: calculated and drawn results. Descriptions of instructions that offer only the

Calculate

output choice show the

calculated results on the home screen.

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

Float

or a different fixed-decimal setting, your

output may differ from the output in the examples.

Be sure to turn off the y= functions before drawing results.

To remove the menu from a drawing, press :.

Ztest

Z-Test

This one-sample Z-test, shown as

in the editor, performs a hypothesis test for a single unknown population mean m when the population standard deviation

is known. It tests the null hypothesis H0: m=

alternatives below.

against one of the

Input

Calculate Results

mƒm

: m<

: m>

ƒm

(m:

)

(m:<

(m:>

)

In the example:

L1=

{299.4 297.7 301 298.9 300.2 297}

Data Stats

Drawn Results

Assembly Language Programming: Inferential Statistics and Distribution Functions

TTest

T-Test

This one-sample t-test, shown as

in the editor, performs a hypothesis test

for a single unknown population mean m when the population standard deviation

is unknown. It tests the null hypothesis H

below.

: m=

against one of the alternatives

Input

Calculate Results

mƒm

: m<

: m>

ƒm

(m:

)

(m:<

(m:>

)

In the example:

TEST=

{91.9 97.8 111.4 122.3 105.4 95}

Data Stats

Drawn Results

Assembly Language Programming: Inferential Statistics and Distribution Functions

Zsam2

This two-sample Z-test, shown as the means of two populations ( both population standard deviations ( H

is tested against one of the alternatives below.

m m m

1ƒm2

(m1:ƒm2) (m1:<m2)

(m1:>m2)

2-SampZTest

and

) based on independent samples when

and

In the example:

in the editor, tests the equality of

) are known. The null hypothesis

Input

Calculate Results

LISTA= LISTB=

{154 109 137 115 140} {108 115 126 92 146}

Data Stats

Drawn Results

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