Texas Instruments TI-86 - ViewScreen Calculator Manuale

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

1 Start the TI-86 Graph Link on

your computer.

WLink86.exe

2 Turn on your TI-86 and display

the home screen.

-l

3 Click on the Send button on the

TI-86 Graph Link toolbar to

display the Send dialog box.

4 Specify the statistics program

file as the file you want to send.

infstat1.86g

5 Send the program to the TI-86.

The program and its associated

executable file become items on

the PRGM NAMES menu.

6 Exit Graph Link.

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 Infstats is the only assembly language program installed

on your TI-86. The position of STAT on the MATH menu may vary, depending on

how many other assembly language programs are installed.

1 Select Asm( from the CATALOG

to paste it to a blank line on the

home screen.

-w&

#(move 4to

Asm( ) b

2 Select Infstat from the PRGM

NAMES menu to paste Infstats

to the home screen as an

argument.

8&(select

Infstat E

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.

Other files associated with

the assembly language

program (

exstats,exstats2,

statedit

) appear on the

PRGM NAMES

menu, but you

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.

Assembly Language Programming: Inferential Statistics and Distribution Functions

3 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.

4 Continue the installation. Your

version number may differ from

the one shown in the example.

5 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, STAT becomes the last item on the MATH menu.

NUM PROB ANGLE HYP MISC 4INTER STAT

Inferential Statistics and Distribution Menu

The STAT Menu -Œ/'

TESTS DISTR DRAW FUNC Uninst 4RsltOn RsltOf

Inferential Distribution Uninstall Results Off

Statistics Shading Instruction (Default)

Test Editors

Distribution Inferential Results On

Functions Statistics (Intermediate calculation

Test Functions results display)

Uninstalling the Inferential Statistics and Distribution Features

1 Display the STAT menu, and

then select Uninst.

-Œ/'

2 If you are sure you want to

uninstall, select Yes from the

confirmation menu. The STAT

menu is removed and the home

screen is displayed. Your version

number may differ from the one

shown in the example.

)

The variables that will be

overwritten are listed on

page 26.

If other assembly language

programs are installed,

STAT

may be in a menu cell other

than

-Œ/'

When you uninstall the

inferential statistics and

distribution features, the

statistics assembly language

programs (

Infstats, exstats,

exstats2,

and

statedit

)

remain in memory, but the

STAT

option is removed from

the

MATH

menu.

Assembly Language Programming: Inferential Statistics and Distribution Functions

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

1 Select DELET from the MEM

menu.

-™'

2 Select PRGM from the MEM

DELET menu.

3 Move the selection cursor to

Infstats, and then delete it.

#(as needed)

4 Move the selection cursor to

exstats and then delete it. Scroll

down and delete exstats2 and

statedit.

#(as needed)

5 Display the home screen. :

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 tdistribution 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

1 Create a new list column. The Ø

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.

-š'}

2 Enter the list name at the Name=

prompt. The list to which you

will store the women’s height

data is created.

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

3 Move the cursor onto the first

row of the list. HGHT(1)= is

displayed on the bottom line.

†

Deleting the program does

not delete the variables

associated with the program.

Assembly Language Programming: Inferential Statistics and Distribution Functions

4 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.

66 Ë7 Í

5 Display the inferential statistics

editor for TIntl (TInterval) from

the STAT TESTS menu.

.-Œ

/'&/

(

6 Select Data in the Inpt field. If Stats is selected,

press |Í

7 Enter the test requirements:

¦ Set alpha-lock and enter the

List name.

¦ Enter 1 at the Freq= prompt.

¦ Enter a 99 percent

confidence level at the

C-Level= prompt.

†11

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

†1

†Ë99

8 Calculate the test. The results

are displayed on the home

screen.

Note: Press ., :, or

bto clear the results from

the screen.

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 þused to compute this

interval. The third line gives the sample standard deviation Sx. The bottom line

gives the sample size n.

To obtain a more precise bound on the population mean mof women’s heights,

increase the sample size to 90. Use a sample mean þof 64.5 and sample standard

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

Stats (summary statistics) input option.

Assembly Language Programming: Inferential Statistics and Distribution Functions

9 Display the inferential statistics

and distribution editor for TIntl

and select Stats in the Inpt field.

:-Œ

/'&/

(~Í

JEnter the test requirements:

¦ Store 64.5 to þ

¦ Store 2.8 to Sx

¦ Store 90 to n

†64 Ë5Í

2Ë8Í

90 Í

KCalculate the test. The results

are displayed on the home

screen.

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

with a mean mof 65 inches and a standard deviation σof 2.5 inches, what height is

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

LDisplay the STAT DISTR

(Distributions) menu.

‘yŒ

/''

MPaste invnm( to the home

screen. (invnm stands for

Inverse Normal.)

(

NEnter .95 as the area, 65 as µ,

and 2.5 as σ.

Ë95 ¢65 ¢2Ë

5¤Í

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.

OSet the window variables to these

values:

xMin=55 yMin=L.05 xRes=1

xMax=75 yMax=.2

xScl=2.5 yScl=0

PDisplay the STAT DRAW menu. .yŒ

/'(

QPaste ShdNm( to the home

screen. (ShdNm stands for Shade

Normal.)

The parameters are

invnm(

area

[

, m, s

]).

Assembly Language Programming: Inferential Statistics and Distribution Functions

RThe answer (Ans 69.1121340648)

from step 14 is the lower bound.

1å99 is the upper bound. The

normal curve is defined by a

mean µof 65 and a standard

deviation σof 2.5.

y¡¢1C

99 ¢65 ¢2Ë5

SPlot and shade the normal curve.

Area= is the area above the 95th

percentile. low= is the lower

bound. 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. ANOVA(

does not have an editor screen.

Using an Inferential Statistics Editor

This example uses the inferential statistics editor for TTest.

1 Select a hypothesis test or

confidence interval from the

STAT TESTS menu. The

appropriate editor displays.

-Œ/'

&'(displays

the TTest editor)

2 Select Data or Stats input, if the

selection is available.

"or !b

3 Enter real numbers, list names,

or expressions for each

argument in the editor. See the

input descriptions table on

page 24.

#65 #

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

4 Select the alternative hypothesis

against which to test, if the

selection is available.

The parameters are

ShdNm(

lowerbound,

upperbound

[

, m, s

])

Select

Data

to enter the data

lists as input. Select

Stats

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.

Assembly Language Programming: Inferential Statistics and Distribution Functions

5 Select Calc or Draw (when Draw

is available) to execute the

instruction.

&or '

¦ When you select Calc, the

results are displayed on 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.

1 Turn RsltOn (Results On).

Note: The default is RsltOf

(Results Off).

-Œ/'

/&b

2 Select the instruction from the

STAT FUNC menu.

:/)'

(for the TTest

instruction)

3 Input the syntax for each

hypothesis test and confidence

interval instruction. Complete

the syntax by using one of the

options below:

D65 P65.68 P

2.71735165188 P

10 P0P

¦ 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

use RsltOf.

0Eb

– or –

¦ Enter 1 as the last parameter

to display the results in a

graph. The graph is drawn

whether you use RsltOn or

RsltOf.

You can remove the menu

from the bottom of the screen.

1Eb

Select

Yes

for the

Pooled option, if the selection

is available. The Pooled

option is available for

Tsam2

and

TInt2

only. Press

to select an option.

¦ Select

if you do not

want the variances pooled.

Population variances can

be unequal.

¦ Select

Yes

if you want the

variances pooled.

Population variances are

assumed to be equal.

This example uses summary

statistics. See pages 35-38

for a list of

FUNC

(Function)

menu parameters.

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 4RsltOn RsltOf

ZTest TTest Zsam2 Tsam2 ZPrp1 4ZPrp2 ZIntl TIntl ZInt2 TInt2

4ZPin1 ZPin2 Chitst FSam2 TLinR

4ANOVA

Test Name Description Function

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

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

Zsam2 Two-sample Z-test Test comparing two m’s, known s’s

Tsam2 Two-sample t-test Test comparing two m’s, unknown s’s

ZPrp1 One-proportion Z-test Test for one proportion

ZPrp2 Two- proportion Z-test Test comparing two proportions

ZIntl One-sample Zconfidence interval Confidence interval for one m,

known s

TIntl One-sample tconfidence interval Confidence interval for one m,

unknown s

ZInt2 Two-sample Zconfidence

interval

Confidence interval for difference of

two m’s, known s’s

TInt2 Two-sample tconfidence interval Confidence interval for difference of

two m’s, unknown s’s

ZPin1 One-proportion Zconfidence

interval

Confidence interval for one

proportion

ZPin2 Two-proportion Zconfidence

interval

Confidence interval for difference of

two proportions

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

FSam2 Two-sample Û-test Test comparing two s’s

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

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

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

This one-sample Z-test, shown as Z-Test in the editor, performs a hypothesis test

for a single unknown population mean mwhen the population standard

deviation

is known. It tests the null hypothesis H0: m=m0against one of the

alternatives below.

¦ Ha: mƒm0(m:ƒm0)

¦ Ha: m<m0(m:<m0)

¦ Ha: m>m0(m:>m0)

In the example:

L1={299.4 297.7 301 298.9 300.2 297}

Data Stats

Input

Calculate

Results

Drawn

Results

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