Starbucks offers benefits to their employees that work more than 20 hours per week. The CEO is proud of this new policy and wants to ensure that the average worker works more than 20 hours a week. The company has decided to sample 10 employees and ask them how many hours they work per week. The following are the responses they received:

23, 18, 20, 26, 27, 30, 16, 18, 20, 28

Conduct the appropriate hypothesis test to see if the mean hours worked per week is more than 20 hours based on these results.

(a)State the null and alternative hypotheses.

(b)Calculate the appropriate test statistic for this test. What does this test statistic measure?

(c)Calculate the p-value for this test statistic.

(d)Starbucks has not decided on a value for alpha. Suggest a value for alpha that would cause the company to believe that the mean hours worked is more than 20 hours. Explain your choice for alpha.

(e)Sketch the distribution of test statistic when the null is true, and shade the area that corresponds to the p-value.