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For many years "working full-time" has meant 40 hours per week. Nowadays it seems that corporate employers expect their employees to work more than this amount. A researcher decides to investigate this hypothesis.

Claim 1: The average time full-time corporate employees work per week is 40 hours.
Claim 2: The average time full-time corporate employees work per week is more than 40 hours.

To substantiate his claim, the researcher randomly selects 250 corporate employees and finds that they work an average of 47 hours per week with a standard deviation of 3.2 hours.

In order to assess this evidence, we need to find:

how likely it is in a sample of 250 we will find that the mean number of hours per week corporate employees work is as high as 47.
how likely it is that the true mean number of hours per week corporate employees work is 40.
how likely it is that the true mean number of hours per week corporate employees work is more than 40.
how likely it is that in a sample of 250 we will find that the mean number of hours per week corporate employees work is as high as 47 if the true mean is 40.

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