**Procedures:**

1. Sample mean, sample standard deviation, population standard deviation, sample median, Q1, Q3, etc

2. Normal: Find P(X<=x) or P(a<=X<=b) where X is normal with parameters mu and sigma

3. Binomial: Find P(X<=x) and P(X=x) where X is binomial with parameters n and p

4. Poisson: Find P(X<=x) and P(X=x) where X has a Poisson distribution with mean mu.

5. Student's t, Chi-square, or F distribution: Find P(X<=x) for given degrees of freedom

6. Normal quantile: Find x such that P(X<=x)=p for a given p where X is normal with mu and sigma

8. Normal (Z) confidence intervals for a mean (if sigma is known)

9. Student-t confidence intervals for a mean (if sigma is not known and the data is normal)

10. Population proportion: Normal (Z) confidence intervals for p given a sample proportion

11. 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).

12. 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).

13. Correlation coefficients and simple linear regression

14. One-way ANOVA for d samples

**1. Calculating the sample mean, sample standard deviation, population
standard deviation, sample median, Q1, Q3, etc**

**1a. Use of variables in TI-83, for example to find a 95%
Z-confidence interval from a sample mean and sample standard
deviation,**
Go to top of this page

For example, suppose that you know Xbar=26.13, Sx=4.815, and n=10 and want to find the confidence interval (Xbar-1.95996Sx/root(10), Xbar+1.95996Sx/root(10)) without entering Xbar, 1.95996, and Sx twice. First define a variable W for the confidence-interval half-width HWID by entering 1.95996*4.815/root(10 (with X for *, Div for /, and (2nd)x^2 for root( ) then enter STO W (ALPHA(-) for W). This displays HWID and also stores it in the variable W. Any of the alphabetical characters A-Z can be used as a TI-83 variable name. Enter W (ALPHA(-)) ENTER to display W.

**2. Find P(X<=x) or P(a<=X<=b) where X has a normal
distribution with parameters**
Go to top of this page

`normalcdf(`

`normalcdf(a,b,mu,sigma)`

. That is, after
`normalcdf(`

, enter `A`

then COMMA (the key with a
comma on it) then `B`

then COMMA then `mu`

then
COMMA then `sigma`

then ENTER. You can enter `)`

(the right-parenthesis button) before you press ENTER, but it is not
necessary. The probability will appear.
`)`

(right-parenthesis) then ENTER. The number
0.43319.... should appear.
`-1E99`

) in place of
the lower bound. Here
`-`

is the ``unary'' minus that appears as
`(-)`

on the TI-83 keyboard and NOT the ``binary'' minus that
appears on the right-most column of buttons and as used for expressions
like 13-17, and
`E`

is entered by entering 2nd COMMA for EE.
`-1E99`

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. 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.
**3. Find P(X<=x) where X has a binomial distribution with
parameters n and p:**
Go to top of this page

`binomcdf(`

and press ENTER . Select
`binompdf(`

for P(X=x). As a shortcut, if you entered
(2nd)VARS, enter A (ALPHA(MATH)) for `A:binomcdf(`

or 0 for
`0:binompdf(`

.
`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:** Olders TI-83s may crash if you try to calculate a binomial
cumulative probability with n=1000 . Use the normal approximation to
the binomial for values of n that are this large.

**4. Poisson: Find P(X<=x) and P(X=x) where X has a Poisson
distribution with mean mu.**
Go to top of this page

`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.
**5. Find P(X<=x) where X has a Student's t, Chi-square, or F
distribution**
Go to top of this page

`5:tcdf(,`

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

or 9 for
`9:Fcdf(`

,
`tcdf`

and `X`^{2}cdf

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

.
`Fcdf`

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

.
`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 two-sample T-test. If you enter fractional numbers of
degrees of freedom for `Fcdf(`

on current TI-83s, you appear to
get error messages.
**6. Normal quantiles: Find x such that P(X<=x)=p for a
given p where X has a normal distribution with parameters**
Go to top of this page

`3:invNorm(`

.
`invNorm(`

is
`invNorm(pp,mu,sigma ENTER`

is or `invNorm(pp ENTER`

for a standard normal quantile (mu=0 and sigma=1).
`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.
**7. Student-t, Chi-square, and F-distribution
quantiles: Find x such that (for example) P(T<x)=p for a given p where
T has a Student-t (or Chi-square or F distribution).**
Go to top of this page

This is harder than finding normal quantiles, and makes use of general Equation Solver routines on the TI-83 in combination with the built-in functions for the Student-t, Chi-square, or F-distribution cdfs.

For example, to find the 5% upper critical value (same as the 0.95 quantile) for a Student-t distribution with 8 degrees of freedom,

`eqn:0=`

on the
second line of the screen. Enter 0.95 then (binary) Minus (the minus key
on the right-hand column of buttons), then
`tcdf(`

by entering
(2nd)VARS then 5 for `5:tcdf(`

. DO NOT spell out ``tcdf('' on
the TI-83 keypad. You should now see `eqn:0.95-tcdf(`

on the
second line of the TI-83 screen.
`left-rt=0`

, which is a sign that it has
checked the answer. The returned number for X will be the desired quantile.
`Fcdf(`

) then 0 then
COMMA then X (that is, ALPHA(STO)) then COMMA then 5 then COMMA then 10
then ENTER. After the SOLVER screen appears, make sure that the cursor is
on the X= row and enter SOLVE ((ALPHA)ENTER). After a number of seconds
the number 5.636326... will appear followed by `left-rt=0`

. You
can check F(5,10,0.01)=5.636326... from Stat tables.
**8. Normal (Z) confidence intervals for a mean (if sigma is known)**
Go to top of this page

To find a confidence interval for the mean from a sample X1, X2, ... Xn, you have two choices for entering the sample data into the TI-83, either (a) enter the numbers X1,X2,...,Xn into one of the TI-83 list registers (for example, L1) or (b) enter the sample statistics Xbar, Sx, and n directly.

To find a normal (Z) confidence interval for the mean by entering the X1,X2,...,Xn explicitly,

`7:ZInterval`

`sigma=`

, make sure that `List:`

has the
correct list register (for example, L1) and that `Freq=1`

. Enter
the size of the confidence interval (that is, 0.95 for a 95% confidence
interval). Highlight `Calculate`

and press ENTER.
To find a normal (Z) confidence interval for the mean by entering sigma, Xbar, and n explicitly,

`7:ZInterval`

`Calculate`

and press ENTER.
**9. Student-t confidence intervals for a mean (if sigma is not known and
the data is normal)**
Go to top of this page

To find a confidence interval for the mean from a sample X1, X2, ... Xn, you have two choices for entering the sample data into the TI-83, either (a) enter the numbers X1,X2,...,Xn into one of the TI-83 list registers (for example, L1) or (b) enter the sample statistics Xbar, Sx, and n directly.

To find a Student-t confidence interval for the mean by entering the X1,X2,...,Xn explicitly,

`8:TInterval`

`List:`

has the correct list register (for example, L1) and
that `Freq=1`

. Enter the size of the confidence interval (that
is, 0.95 for a 95% confidence interval). Highlight `Calculate`

and press ENTER.
To find a Student-t confidence interval for the mean by entering Xbar, Sx, and n explicitly,

`8:TInterval`

`Calculate`

and press ENTER.
**10. Normal (Z) confidence intervals for a population
proportion (p) given a sample proportion**
Go to top of this page

`A:1PropZint`

**11. One-sample and Two-sample Z tests:**
Go to top of this page

**12. One-sample and Two-sample T tests:**
Go to top of this page

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**.

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

`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)`

.
`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 step (iii), then r
**14. One-way ANOVA for d samples**
Go to top of this page

After you have turned on the TI-83 and possibly reset or cleared it,

`F:ANOVA(`

. 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 March 13, 2008