An automobile shop manager timed six employees and found that the average time it took them to change a water pump was 18 minutes. The standard deviation of the sample was 3 minutes. Find the 99% confidence interval of the true mean.
From the statement of the problem we have n = 6, = 18, and the sample standard deviation, s = 3. We are looking for a 99% confidence interval of the mean where n < 30 and the standard deviation is unknown. Thus we use the TI83/84 TInterval function.
Press STAT and right arrow twice to TESTS. Arrow down to 8:TInterval and press ENTER to select it. If Stats is not selected, right arrow and press ENTER to select it. Arrow down once and enter 18 for . Arrow down once and enter 3 for . Arrow down once and enter 6 for n. Arrow down once and type .99 for C-level
Arrow down one last time and press ENTER. The calculation will now be preformed, and the results are shown below.
The 99% confidence interval of the mean is 13.062 < < 22.938.
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