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
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).
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
H0:muX=mu0 (one sample) or else
H0:muX=muY (two samples).
12. 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).
13. Correlation coefficients and simple linear
regression
14. One-way ANOVA for d samples
RESETTING the TI-83: Press (2nd)+ (for MEM) and then enter
EITHER 4:ClrAllLists or 5:Reset depending on the model of the TI-83.
Follow the instructions. To do this quickly, enter EITHER (2nd)+ (for MEM)
4:ClrAllLists ENTER (TI-83 Plus etc) OR (2nd)+ (MEM) 5 then 1 then 2
(TI-83 etc).
1. Calculating the sample mean, sample standard deviation, population
standard deviation, sample median, Q1, Q3, etc
To do this, you must first enter a list of numbers in one of the TI-83's
spreadsheet-like list registers. First,
1a. Use of variables in TI-83, for example to find a 95%
Z-confidence interval from a sample mean and sample standard
deviation,
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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
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3. Find P(X<=x) where X has a binomial distribution with
parameters n and p:
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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.
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5. Find P(X<=x) where X has a Student's t, Chi-square, or F
distribution
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6. Normal quantiles: Find x such that P(X<=x)=p for a
given p where X has a normal distribution with parameters
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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).
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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,
8. Normal (Z) confidence intervals for a mean (if sigma is known)
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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,
To find a normal (Z) confidence interval for the mean by entering sigma,
Xbar, and n explicitly,
9. Student-t confidence intervals for a mean (if sigma is not known and
the data is normal)
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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,
To find a Student-t confidence interval for the mean by entering Xbar, Sx,
and n explicitly,
10. Normal (Z) confidence intervals for a population
proportion (p) given a sample proportion
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11. One-sample and Two-sample Z tests:
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12. One-sample and Two-sample T tests:
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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 (X1,Y1),
(X2,Y2),
(X3,Y2), ...,
(Xn,Yn), find
14. One-way ANOVA for d samples
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After you have turned on the TI-83 and possibly reset or
cleared it,
Last modified March 13, 2008
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.
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 .
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: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 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.
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.
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.
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.
7:ZInterval
Calculate
and press ENTER.
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.
8:TInterval
Calculate
and press ENTER.
A:1PropZint
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 r2 and r will also appear.
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.