A recent survey from PayScale found that 46% of U.S. workers— roughly 22 million—are underemployed, either working part-time or at jobs that don’t allow them to use their education or skills. Suppose that the numbers of hours worked in the past week were collected from a random sample of 28,585 of these workers. The data collected in this survey are provided in the file Under Employed.

a. What is the sample mean number of hours worked by underemployed U.S. workers? 

b. Using 99% confidence, what is the margin of error? 

c. Using the results from parts (a) and (b), develop the 99% confidence interval estimate of the mean number of hours worked by underemployed U.S. workers. 

d. If the mean hours worked by underemployed U.S. workers during the same week one year ago was 35.6, what would the confidence interval in part (c) lead you to conclude about last week?