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Testing to see if the mean is less than a fixed number

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During recent seasons, Major League Baseball has been criticized for the length of the games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following times to completion. (Note that the minutes have been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes is reported at 2.40 hours.)

2.98, 2.40, 2.70, 2.25, 3.23, 3.17, 2.93, 3.18, 2.80, 2.38, 3.75, 3.20, 3.27, 2.52 2.58, 4.45, 2.45

Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05 significance level.

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Solution Preview

What we need to do is calculate the mean and standard deviation of our sample and then perform a t-test for the following hypothesis.

H0: Mean = 3.5
H1: Mean < 3.5

I have calculated the mean of the sample to be 2.955. The standard deviation of the sample, I have calculated to be equal to .5596. I will assume that you ...

Solution Summary

A step-by-step solution illustrates the process of performing a hypothesis test. A 1-tailed t-test is used.