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# One Sample Test of Hypothesis

42. 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. Estimate the p-value

#### Solution Preview

Please see the attached file. I have corrected the question based on the attachment that you have provided.
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 2.4 2.7 2.25 3.23 3.17 2.93 3.18 2.8
2.38 3.75 3.2 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.

I ) Calculation of sample mean and standard deviation

Mean and standard deviation

X= X 2 =
2.98 8.8804
2.4 5.76
2.7 7.29
2.25 5.0625
3.23 10.4329
3.17 10.0489
2.93 ...

#### Solution Summary

Tests the hypothesis that the mean time for a game is less than 3.50 hours.

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