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Calculators and computers can easily calculate any Student's t-probabilities. The TI-83,83+, and 84+ have a tcdf function to find the probability for given values of t . The grammar for the tcdf command is tcdf(lower bound, upper bound, degrees of freedom). However for confidence intervals, we need to use inverse probability to find the value of t when we know the probability.
For the TI-84+ you can use the invT command on the DISTRibution menu. The invT command works similarly to the invnorm. The invT command requires two inputs:
invT(area to the left, degrees of freedom) The output is the t-score that corresponds to the area we specified.
The TI-83 and 83+ do not have the invT command. (The TI-89 has an inverse T command.)
A probability table for the Student's t-distribution can also be used. The table gives t-scores that correspond to the confidence level (column) and degrees of freedom (row). (The TI-86 does not have an invT program or command, so if you are using that calculator, you need to use a probability table for the Student's t-Distribution.) When using a
t -table, note that some tables are formatted to show the confidence level in the column headings, while the column headings in some tables may show only corresponding area in one or both tails.
A Student's t table (See
[link] ) gives
t -scores given the degrees of freedom and the right-tailed probability. The table is very limited.
Calculators and computers can easily calculate any Student's t-probabilities.
If the population standard deviation is not known , the error bound for a population mean is:
The format for the confidence interval is:
$(\overline{x}-EBM,\overline{x}+EBM)$ .
To calculate the confidence interval directly:
Press STAT.
Arrow over to TESTS.
Arrow down to 8:TInterval and press ENTER (or just press 8).
Suppose you do a study of acupuncture to determine how effective it is in relieving pain. You measure sensory rates for 15 subjects with the results given. Use the sample data to construct a 95% confidence interval for the mean sensory rate for the population (assumed normal) from which you took the data.
The solution is shown step-by-step and by using the TI-83, 83+, or 84+ calculators.
Press
STAT
and arrow over to
TESTS
.
Arrow down to
8:TInterval
and press
ENTER
(or you can just press
8
).
Arrow to
Data
and press
ENTER
.
Arrow down to
List
and enter the list name where you put the data.
There should be a 1 after
Freq
.
Arrow down to
C-level
and enter 0.95
Arrow down to
Calculate
and press
ENTER
.
The 95% confidence interval is (7.3006, 9.1527)
When calculating the error bound, a probability table for the Student's t-distribution can also be used to find the value of t . The table gives t -scores that correspond to the confidence level (column) and degrees of freedom (row); the t -score is found where the row and column intersect in the table.
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