According to the Census Bureau, 2,475,780 people are employed by the federal government in the United States (U.S. Census Bureau website, May 30, 2016). Suppose that a random sample of 3500 of these federal employees was selected and the number of sick hours each of these employees took last year was collected from an electronic personnel database. The data collected in this survey are provided in the DATAfile named FedSickHours. Based on historical data, the population standard deviation can be assumed to be known with σ = 34.5.

a. What is the point estimate for the mean number of sick hours taken by federal employees last year?

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

c. Using the results from part (a) and part (b), develop the 99% confidence interval estimate of the mean number of sick hours taken by federal employees last year.

d. If the mean sick hours federal employees took two years ago was 62.2, what would the confidence interval in part (c) lead you to conclude about last year?