Generating Confidence Intervals with a TI-83Plus Graphing Calculator
I recently covered confidence intervals in my statistics class. While the formulas for constructing confidence intervals are fairly simple and should be learned by students, variaous forms of technology to automate the simple computations are available. One such form of technology is provided by the TI-83Plus graphing calculator. In this posting, I'll illustrate the process of constructing confidence intervals with the TI-83Plus graphing calculator, using examples from the course textbook, Essentials of Statistics 2nd Edition by Mario F. Triola, Pub. Pearson/Addison Wesley. In each example, I'll show how to obtain a confidence interval for the population mean, μ. Read more for the examples.
In the example beginning on the bottom of Page 289, you are given that a random sample 106 body temperatures produces a mean of
=98.20 degrees F. Assuming that the population standard deviation, σ is known to be 0.62 degrees F, find a 95% confidence interval estimate of the true population mean, μ. Since σ is known and we have a large sample, we use a normal distribution to obtain the confidence interval ("Z-interval").
Next, in the ZInterval window, select Stats, and enter the values given the in exercise in the appropriate fields, as shown below.
Next, select Calculate at the bottom of the ZInterval window, and press ENTER to obtain the desired confidence interval.
Example 2. Population standard deviation, σ is known.
To compute a confidence interval from raw data, let's consider the cotinine levels (in ng/ml) of a random sample of 40 smokers as shown in Table 2-12 on Page 89. Assuming that the population standard deviation, σ is known to be 119.5, find a 90% confidence interval estimate of the true population mean, μ.
Press STAT, and select
EDIT-->1:Edit
Then
enter the 40 cotinine values under
L1, as
shown.
Next, press
STAT and
select
TESTS-->ZInterval.
This time, select
Data for
the Inpt
field, enter 119.5 for the population standard
deviation, and 0.90 for C-level (the confidence
level).
Finally, select
Calculate
and press ENTER
to obtain the desired confidence
interval.
Example 3. Population standard deviation, σ is unknown.
Suppose that in our first example, in which we were given that a random sample of 106 body temperatures produced a mean of =98.20 degrees F, the true population standard deviation is unknown. Suppose further that a sample standard deviation of s= 0.62 degrees F was produced. To find a 95% confidence interval estimate of the true population mean, μ we we use a t-distribution to obtain the confidence interval ("t-interval") . As an exercise, check that the assumptions required to use the t-distribution are met.
Press
STAT,
and select
TESTS-->8:TInterval
In the
TInterval
window, select
Stats,
and enter the given values in the appropriate fields, as shown.
Next, select
Calculate
and press the
ENTER
key to obtain the desired confidence
interval.
Example 4. Population standard deviation, σ is unknown.
In Exercise 17 on Page 312 you're given 7 values of nitrogen-oxide emissions (in grams per mile): 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, and 0.15. To find a 98% confidence interval estimate of the true population mean, μ you must use a t-distribution to obtain the confidence interval ("t-interval") . As an exercise, check that the assumptions required to use the t-distribution are met.
Press the
STAT
key, select
EDIT-->1:Edit,
and enter the 7 values under
L1, as
shown.
After
you've entered the data, press the
STAT key
again, and select
TESTS-->TInterval.
In the
TInterval
window, select
Data and
enter the 0.98 for the confidence level
(C-Level),
as shown.
Finally, select
Calculate
and press the
ENTER
key to obtain the desired confidence
interval.
Posted: Monday - December 04, 2006 at 09:35 AM
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Published On: May 23, 2008 09:10 AM