You are recently hired at a sleep research company to perform statistical calculations. Your boss has assigned you two hypothesis tests to run.

Part One - Hypothesis Tests

Complete a hypothesis tests of the two situations listed below by:

Constructing an 8-step hypothesis test, showing all calculations,

Including both the critical value method and the p-value method in your calculations.

Using the correct terminology and interpretation of the resulting confidence interval for each test.

Hypothesis Test - Situation 1

It has been reported that the mean amount of sleep that adults receive is 7 hours per night. Your boss has asked you to look into this statistic by running your own study. You gather 49 adults and find the following information. The mean amount of sleep was 6.2 hours with a standard deviation of 1.8 hours. Based on your results, you claim that adults receive less than 7 hours of sleep. Test your claim with a 0.05 significance level.

Hypothesis Tests - Situation 2

Your boss also would like you to look at average sleep for a specific age range (between 35 and 44 years of age). It has been previously reported that 38.3% of adults in this age range receive the recommended amount of sleep per night (at least 7 hours). You decide to test this claim by gathering 32 adults between the ages of 35 and 44 years old. In the sample, you find that 15 of the participants receive at least 7 hours of sleep. Test the claim that more than 38.3% of adults get the recommended amount of sleep per night with a significance level of 0.01.

Part Two - Hypothesis Errors

After you have completed your hypothesis tests, in a separate paragraph,

Explain the possible error(s) that could have occurred and what they imply for each test.

Explain how you might prevent the error(s) from occurring in future hypothesis tests.