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Solving for the Significance Level

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Scenario: 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

Let us go through the steps:

The first step in hypothesis testing is to specify the null hypothesis (Ho) and the alternative hypothesis (Ha)

Ho: The average game is 3.5 hours (u=3.5)
Ha: The average game is less then 3.5 hours (u<3.5)

The next step is to select a significance level. Typically the 0.05 as stated in the question.

Next we calculate the test statistic:

The formula would be: the average of our sample (x) - the average stated (x bar) / variability (standard deviation divide by square root ...

Solution Summary

The solution examines solving significance levels during recent major league baseball seasons.