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
H_{0}:mu_{X}=mu_{0} (one sample) or else
H_{0}:mu_{X}=mu_{Y} (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
H_{0}:mu_{X}=mu_{0} (one sample) or else
H_{0}:mu_{X}=mu_{Y} (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:**

**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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**In Microsoft Excel:**
(See Math320 Excel Notes)

**If you have a TI-83**:

`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 .
**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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**In Microsoft Excel**:
(See Math320 Excel Notes)

**If you have a TI-83**:

`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.
**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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**In Microsoft Excel**:
(See Math320 Excel Notes)

**Using a TI-83**:

`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.
**6. One-sample and Two-sample Z tests:**
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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.

**Using a TI-83**:

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**.

**7. Poisson: Find P(X<=x) and P(X=x) where X has a
Poisson distribution with mean mu.**
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**In Microsoft Excel:**
(See Math320 Excel Notes)

**If you have a TI-83**:

`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.
**8. Find P(X<=x) where X has a Student's t, Chi-square, or F
distribution**
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**In Microsoft Excel**:
(See Math320 Excel Notes)

**Using a TI-83**:

`5:tcdf(,`

, 7 for
`7:X`^{2}cdf(

, or 9 for `9:Fcdf(`

,
`tcdf`

and
`X`^{2}cdf

is
`(Function)(Lower,Upper,df)`

. The syntax for
`Fcdf`

is `Fcdf(Lower,Upper,numdf,denomdf)`

. For
example, to find P(X>=1.645) where X has a Student's t-distribution
with 11 degrees of freedom, enter (in order) 1.645 then COMMA then 1
2ndCOMMA (for EE) 99 (for 1E99) then COMMA then 11 then )(right
parenthesis) then ENTER. The number 0.0641075923 should appear.
Chi-square and F distributions are restricted to nonnegative values, so
that you can enter 0 (zero) in place of -1E99 for the lower bound for
`7:X`^{2}cdf(

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(`

does not accept fractional
numbers of degrees of freedom on my TI-83, but may on newer calculators.
**9. One-sample and Two-sample T tests:**
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Click on Tools then Data Analysis.... then one of

Follow the directions. See the Math320 Excel Notes for more details.

**Using a TI-83**:

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**.

**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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**In Microsoft Excel**:
(See Math320 Excel Notes)

`Statistical`

menu. Excel does not seem to offer any other
help on confidence intervals.
**Using a TI-83**:

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?

**11. Given data X _{1}, X_{2}, ...
X_{n}, find a ``Student's-t'' confidence interval for E(X)
based on the assumption that X_{i} are normal:**

**Using a TI-83**:

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.

**12. Do a one-sample or two-sample t-test**
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**In Microsoft Excel**:
(See Math320 Excel Notes)

**Using a TI-83**:

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.
**13. Given paired data (X _{1},Y_{1}),
(X_{2},Y_{2}),
(X_{3},Y_{2}), ...,
(X_{n},Y_{n}), find
**

**Using a TI-83**:

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 r
**14. One-way ANOVA for d samples**
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**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.
**Using a TI-83**:

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.

Last modified July 23, 2001