Texas Instruments TI-86 - ViewScreen Calculator Manual

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
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.
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
t
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
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.
b
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
4
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)
b
4 Move the selection cursor to
exstats and then delete it. Scroll
down and delete exstats2 and
statedit.
#(as needed)
b
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'}
yp
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]
Í
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
5
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
6
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
6'
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
7
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.
Í
:
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] #
1#
4 Select the alternative hypothesis
against which to test, if the
selection is available.
b
The parameters are
ShdNm(
lowerbound,
upperbound
[
, m, s
])
.
Select
Data
to enter the data
lists as input. Select
Stats
to
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
8
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
No
or
Yes
for the
Pooled option, if the selection
is available. The Pooled
option is available for
Tsam2
and
TInt2
only. Press
"
or
!b
to select an option.
¦ Select
No
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
9
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
10
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
s
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
d
Results
Drawn
Results

Assembly Language Programming: Inferential Statistics and Distribution Functions
11
TTest
This one-sample t-test, shown as T-Test in the editor, performs a hypothesis test
for a single unknown population mean mwhen the population standard deviation
sis unknown. 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:
TEST={91.9 97.8 111.4 122.3 105.4 95}
Data Stats
$$
$$
Input
Calculate
d
Results
Drawn
Results

Assembly Language Programming: Inferential Statistics and Distribution Functions
12
Zsam2
This two-sample Z-test, shown as 2-SampZTest in the editor, tests the equality of
the means of two populations (m1and m2) based on independent samples when
both population standard deviations (s1and
s
2) are known. The null hypothesis
H0: m1=m2is tested against one of the alternatives below.
¦ Ha: m1ƒm2(m1:ƒm2)
¦ Ha: m1<m2(m1:<m2)
¦ Ha: m1>m2(m1:>m2)
In the example:
LISTA={154 109 137 115 140}
LISTB={108 115 126 92 146}
Data Stats
$$
$$
Input
Calculate
d
Results
Drawn
Results

Assembly Language Programming: Inferential Statistics and Distribution Functions
13
Tsam2
This two-sample t-test, shown as 2-SampTTest in the editor, tests the equality of the
means of two populations (m1and m2) based on independent samples when
neither population standard deviation (s1or s2) is known. The null hypothesis
H0: m1=m2is tested against one of the alternatives below.
¦ Ha: m1ƒm2(m1:ƒm2)
¦ Ha: m1<m2(m1:<m2)
¦ Ha: m1>m2(m1:>m2)
In the example:
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
The pooled option is available for Tsam2 and TInt2 only. No means that population
variances can be unequal. Yes means that population variances are assumed to be
equal.
Data Stats
$$
$$
Input
Calculate
d
Results
Drawn
Results

Assembly Language Programming: Inferential Statistics and Distribution Functions
14
ZPrp1
This one-proportion Z-test, shown as 1-PropZTest in the editor, computes a test for
an unknown proportion of successes (prop). It takes as input the count of
successes in the sample xand the count of observations in the sample n. ZPrp1
tests the null hypothesis H0: prop=p0against one of the alternatives below.
¦ Ha: propƒp0(prop:ƒp0)
¦ Ha: prop<p0(prop:<p0)
¦ Ha: prop>p0(prop:>p0)
$
$
Input
Calculate
d
Results
Drawn
Results
phat represents Ç

Assembly Language Programming: Inferential Statistics and Distribution Functions
15
ZPrp2
This two-proportion Z-test, shown as 2-PropZTest in the editor, computes a test to
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). ZPrp2 tests the null hypothesis
H0: p1=p2 (using the pooled sample proportion Ç) against one of the alternatives
below.
Phat represents Çin the editor. Phat1 represents Ç1, and phat2 represents Ç2.
¦ Ha: p1ƒp2(p1:ƒp2)
¦ Ha: p1<p2(p1:<p2)
¦ Ha: p1>p2(p1:>p2)
$
$
Input
Calculate
d
Results
Drawn
Results
phat1 represents Ç1
phat2 represents Ç2
phat represents Ç

Assembly Language Programming: Inferential Statistics and Distribution Functions
16
ZIntl
This one-sample Zconfidence interval, shown as ZInterval in the editor, computes a
confidence interval for an unknown population mean mwhen the population
standard deviation
s
is known. The computed confidence interval depends on the
user-specified confidence level.
In the example:
L1={299.4 297.7 301 298.9 300.2 297}
Data Stats
$$
TIntl
This one-sample tconfidence interval, shown as TInterval in the editor, computes a
confidence interval for an unknown population mean mwhen the population
standard deviation sis unknown. The computed confidence interval depends on
the user-specified confidence level.
In the example:
L6={1.6 1.7 1.8 1.9}
Data Stats
$$
Input
Input
Calculate
d
Results
Calculate
d
Results

Assembly Language Programming: Inferential Statistics and Distribution Functions
17
ZInt2
This two-sample Zconfidence interval, shown as 2-SampZInt in the editor,
computes a confidence interval for the difference between two population means
(m1Nm2) when both population standard deviations (
s
1and
s
2) are known. The
computed confidence interval depends on the user-specified confidence level.
In the example:
LISTC={154 109 137 115 140}
LISTD={108 115 126 92 146}
Data Stats
$$
Input
Calculate
d
Results

Assembly Language Programming: Inferential Statistics and Distribution Functions
18
TInt2
This two-sample tconfidence interval, shown as 2-SampTInt in the editor,
computes a confidence interval for the difference between two population means
(m1Nm2) when both population standard deviations (
s
1and
s
2) are unknown. The
computed confidence interval depends on the user-specified confidence level.
In the example:
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}
SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}
The pooled option is available for TInt2 and Tsam2 only. No means that population
variances can be unequal. Yes means that population variances are assumed to be
equal.
Data Stats
$$
Input
Calculate
d
Results

Assembly Language Programming: Inferential Statistics and Distribution Functions
19
ZPin1
This one-proportion Zconfidence interval, shown as 1-PropZInt in the editor,
computes a confidence interval for an unknown proportion of successes. It takes
as input the count of successes in the sample xand the count of observations in
the sample n. The computed confidence interval depends on the user-specified
confidence level.
$
ZPin2
This two-proportion Zconfidence interval, shown as 2-PropZInt in the editor,
computes a confidence interval for the difference between the proportion of
successes in two populations (p1Np2). It takes as input the count of successes in
each sample (x1and x2) and the count of observations in each sample (n1and n2) .
The computed confidence interval depends on the user-specified confidence level.
$
Input
Input
Calculate
d
Results
Calculate
d
Results

Assembly Language Programming: Inferential Statistics and Distribution Functions
20
Chitst
This test, shown as Chi2-Test in the editor, computes a chi-square test for
association on the two-way table of counts in the matrix you specify at the
Observed prompt. The null hypothesis H0for a two-way table is: no association
exists between row variables and column variables. The alternative hypothesis is:
the variables are related.
Before computing a Chitst, enter the observed counts in a matrix. Enter that
matrix variable name at the Observed prompt in the editor. At the Expected
prompt, enter the matrix variable name to which you want the computed expected
counts to be stored.
Note: Press -‰'[A]
bto select Matrix A from
the MATRX EDIT menu.
$
$Note: Press -‰'[B]
bto display Matrix B.
Input
Calculate
d
Results
Drawn
Results
Matrix
Editor