See Procedures below for specific procedures for Excel or a TI-83.
Procedures:
1. Sample mean, sample standard deviation
2. Population mean, population standard deviation
3. Binomial: Find P(X<=x) and P(X=x) where X is binomial with parameters n and p
4. Normal: Find P(X<=x) or P(a<=X<=b) where X is normal with parameters mu and sigma
5. Inverse normal: Find x such that P(X<=x)=p for a given p where X is normal with mu and sigma
6. One-sample and two-sample Z tests: Given one or two normal samples with known population standard deviations, test H0:muX=mu0 (one sample) or else H0:muX=muY (two samples).
7. Poisson: Find P(X<=x) and P(X=x) where X has a Poisson distribution with mean mu.
8. Student's t, Chi-square, or F distribution: Find P(X<=x) for given degrees of freedom
9. One-sample and two-sample T tests: Given one or two normal samples with UNKNOWN population standard deviations, test H0:muX=mu0 (one sample) or else H0:muX=muY (two samples).
11. Confidence interval for a population mean from a normal sample (Student's t).
12. Do a one-sample or two-sample t-test
13. Correlation coefficients and simple linear
regression
14. One-way ANOVA for d samples
1. Calculating sample mean and sample standard deviations:
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In Microsoft Excel:
(See Math320 Excel Notes)
If you have a TI-83:
RESETTING the TI-83: Press (2nd)+ (for MEM) and then either
4:ClrAllLists or 5:Reset. Follow the instructions. To do this quickly,
enter (2nd)+ (for MEM) then 5 then 1 then 2.
2. Population mean and population standard deviation:
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In Microsoft Excel:
(See Math320 Excel Notes)
If you have a TI-83:
3. Find P(X<=x) where X has a binomial distribution with
parameters n and p:
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NOTE: Some TI-83s will crash if you try to calculate a binomial
cumulative probability with n=1000 . (This is true for the TI-83 in
my office, but is not true for newer TI-83s.) Excel 97 will crash if you
enter n=10,000. Use the normal approximation to the binomial for values of
n that are this large.
4. Find P(X<=x) or P(a<=X<=b) where X has a normal
distribution with parameters
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If you have a TI-83:
5. Find x such that P(X<=x)=p for a
given p where X has a normal distribution with parameters
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Using a TI-83:
6. One-sample and Two-sample Z tests:
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Using a TI-83:
7. Poisson: Find P(X<=x) and P(X=x) where X has a
Poisson distribution with mean mu.
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8. Find P(X<=x) where X has a Student's t, Chi-square, or F
distribution
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Using a TI-83:
9. One-sample and Two-sample T tests:
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Using a TI-83:
10. Given a sample of size n for which x=k have a Property P,
find the 95% confidence interval for the population proportion of
Property P based on a normal approximation.
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Using a TI-83:
11. Given data X1, X2, ...
Xn, find a ``Student's-t'' confidence interval for E(X)
based on the assumption that Xi are normal:
Using a TI-83:
12. Do a one-sample or two-sample t-test
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Using a TI-83:
13. Given paired data (X1,Y1),
(X2,Y2),
(X3,Y2), ...,
(Xn,Yn), find
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Using a TI-83:
14. One-way ANOVA for d samples
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Using a TI-83:
Last modified July 23, 2001
In Microsoft Excel:
(See Math320 Excel Notes)
binomcdf(
and press ENTER . Select
binompdf(
for P(X=x).
binomcdf(numtrials,p,x)
and
binompdf(numtrials,p,x)
. For example, assuming that you
want P(X<=x), wait for a window with binomcdf(
to
appear. Enter n
then COMMA (that is, press the button with
a comma on it) then p
then COMMA then x
then )
(the right-parenthesis button) then ENTER. The probability P(X<=x)
should then appear. For example, If n=50, p=0.055, and x=3, enter 50
then COMMA then 0.055 then COMMA then 3 then ) then ENTER. The number
0.70469... will then appear.
binomcdf(numtrials,p)
. That is, after you get to the window
with binomcdf(
, enter n
then COMMA then
p
then ) (right parenthesis) then ENTER, without the
variable x. A list of the values of P(X<=x) will appear, most of
which will be outside of the calculator window. To view them in a list,
enter STO(arrow)
then (2nd)1 (for List 1) then ENTER, then
enter STAT
then 1 for 1:Edit
. The values of
P(X<=x) will be displayed in a list.
binompdf(
, and press ENTER. When
the window with binompdf(
appears, enter 50 then COMMA then
0.055 then COMMA then (2nd)1 for list L1 then ) (the right-parenthesis
button to close the binompdf(
function) then
STO(arrow)
then (2nd)2 for list 2 then ENTER. If you press
STAT and then 1 for 1:Edit, then the eight probabilities P(X=x) for
x=0,1,2,3,4,5,6,7 will be in list L2 .
In Microsoft Excel:
(See Math320 Excel Notes)
normalcdf(
a
then COMMA (the key with a comma on it) then b
then COMMA then mu
then COMMA then sigma
then
)
(the right-parenthesis button) then ENTER. The probability
will appear. For example, to calculate P(20<=X<=22.7) when mu=20 and
sigma=1.8, enter 20 then COMMA then 22.7 then COMMA then 20 then COMMA
then 1.8 then )
(right-parenthesis) then ENTER. The number
0.43319.... should appear.
)
(right-parenthesis) then ENTER. The answer should be the
same as in (iii).
-1E99
in place of the lower bound. This is
scientific notation for -1 followed by 99 zeroes and is meant to represent
``-infinity''. Similarly, calculate P(X>=x) by entering
1E99
as the upper bound. To enter -1E99
,
(a) press the (-)
key at the bottom of the keypad (this
is the ``unary'' minus sign as in -1 or -5. DO NOT USE the -
key just above the +
key. That is the ``binary'' minus sign,
as in 4-2=2), (b) press 1, (c) press (2nd)COMMA for EE, which
denotes scientific notation for numbers, and (d) enter 99 for the
``exponent''. For example, to calculate P(X<=22.7) for a normal
distribution with mean 20 and standard deviation 1.8, get to a
screen with normalcdf(
as in step (ii). Enter
-1E99
as above then COMMA then 22.7 then COMMA then 20 then
COMMA then 1.8 then )
(right-parenthesis) then ENTER. The
answer 0.93319.... should appear.
In Microsoft Excel:
(See Math320 Excel Notes)
3:invNorm(
.
p
then COMMA (the key with a comma on
it) then mu
then COMMA then sigma
then
)
(the right-parenthesis button) then ENTER. The probability
will appear. For example, to find x such that P(X<=x)=0.666 when mu=20
and sigma=1.8, enter 0.666 then COMMA then 20 then COMMA then 1.8 then
)
(right-parenthesis) then ENTER. The number 20.777... should
appear.
)
(right-parenthesis)
then ENTER. The number 0.42889... should appear.
In Microsoft Excel:
Click on Tools then Data Analysis.... then
Follow the directions. The option and dialog box assume two
samples. I suspect that the second sample can be identically zero, which
would have the same effect as a one-sample test. However, I haven't
checked this. See the Math320 Excel
Notes for more details.
After you have turned on the TI-83 and possibly
reset or cleared it, enter STAT, then TESTS
and then either 1: for a (one-sample) Z test or 3: for a 2-sample
Z test. In either case, the first step will be to either highlite
either Data or Stats.
In Microsoft Excel:
(See Math320 Excel Notes)
poissoncdf(
and press ENTER . Select
poissonpdf(
for P(X=x).
poissoncdf(mu,x)
and poissonpdf(mu,x)
. For
example, assuming that you want P(X<=x), wait for a window with
poissoncdf(
to appear. Enter the value of
mu
then COMMA (that is, press the button with a comma on
it) then x
then ) (the right-parenthesis button) then
ENTER. The probability P(X<=x) should then appear.
In Microsoft Excel:
(See Math320 Excel Notes)
5:tcdf(,
7 for
7:X2cdf(
or 9 for
9:Fcdf(
,
tcdf
and X2cdf
is
(Function)(Lower,Upper,df)
.
Fcdf
is
Fcdf(Lower,Upper,numdf,denomdf)
.
7:X2cdf(
and
9:Fcdf(
.
tcdf(
accepts fractional numbers of
degrees of freedom, so that it can be used to get an exact value for
Satterthwaite's test. Fcdf(
did not accept fractional
numbers of degrees of freedom on my TI-83, but may on newer calculators.
In Microsoft Excel:
Click on Tools then Data Analysis.... then one of
Follow the directions. See the
Math320 Excel Notes for more
details.
After you have turned on the TI-83 and possibly
reset or cleared it, enter STAT, then TESTS and
then either 2: for a (one-sample) T test or 4: for a 2-sample
T test. In either case, the first step will be to either highlite
either Data or Stats.
In Microsoft Excel:
(See Math320 Excel Notes)
Statistical
menu. Excel does not seem to offer any other
help on confidence intervals.
After you have turned on the TI-83 and possibly
reset or cleared it, enter STAT, then TESTS, then
scroll down to A:1-PropZInt. (Alternatively, you can enter STAT, then
TESTS, then ALPHA then MATH . The ALPHA key is a kind of
alternative shift key, which produces A when you enter MATH .)
On the screen that appears, fill in X: (the number of ``successes''),
N: (the number of trials), and make sure that C-Level: is set at
0.95 . Scroll down to CALCULATE and press ENTER. The normal-theory
interval should appear. What confidence interval do you get when you enter
zero (0) for the number of successes?
In Microsoft Excel:
(See Math320 Excel Notes)
After you have turned on the TI-83 and possibly
reset or cleared it, enter STAT, then 1:EDIT, then
enter your sample into list L1.
Enter STAT again, then TESTS, then 8:TInterval. (That is, either scroll
down to this entry and press ENTER or else just enter 8 .) The
next screen should show DATA (if not, highlite it), List:L1 , and
C-Level: 0.95 for a 95% confidence interval. Scroll down to
highlite Calculate and press Enter. The screen may go blank, but after a
few seconds a screen with the confidence interval should appear.
In Microsoft Excel:
(See Math320 Excel Notes)
After you have turned on the TI-83 and possibly
reset or cleared it,
2:T-Test
or
4 for 4:2-SampTTest
. Press ENTER and fill in the screen
that appears. Nothing will happen until you highlight eiter CALCULATE or
DRAW at the bottom of the screen and press ENTER. After a few seconds,
the value of the T-statistic and the P-value will appear.
In Microsoft Excel:
(See Math320 Excel Notes)
After you have turned on the TI-83 and possibly
reset or cleared it,
2nd 0
(for CATALOG), space down to
DiagnosticOn
, press ENTER, and then ENTER again if you see
DiagnosticOn
on a different screen,
4:LinReg(ax+b)
.
When a new screen appears, enter 2nd 1
for list L1,
then COMMA (the comma key), then 2nd 2
for list L2,
then ENTER. After a few seconds the coefficients a,b of the regression
Y=aX+b
will appear. If you entered
DiagnosticOn
in (b), then r2 and r will also
appear.
In Microsoft Excel::
(See Math320 Excel Notes)
Tools
then
Data Analysis...
then Anova: Single factor
. If
the Tools
dropdown menu does not have a Data
Analysis...
option, see Data
Analysis ToolPak. When the ToolPak ANOVA window appears, enter the
range of cells as the upper-left and lower-right corner of a rectangle
of cells.
After you have turned on the TI-83 and possibly
reset or cleared it,
F:ANOVA(
(for example,
by entering ALPHA
then COS
for F). If d=4 for
four treatments, the syntax is ANOVA(L1,L2,L3,L4)
. You will
have to scroll through several screens for the entire output.