A personnel manager is estimating the total number of person-days lost to unexcused absences by hourly workers in the last year. In a random sample of 50 employees drawn without replacement from the 687 hourly workers at the company, records show that the 50 sampled workers had an average of  = 4.3 days of unexcused absences over the past year with a standard deviation of s = 1.26.
a. Find a point estimate of and a 95 percent confidence interval for the total number of unexcused absences by hourly workers in the last year.
b. Can the personnel manager be 95 percent confident that more than 2,500 person-days were lost to unexcused absences last year? Can the manager be 95 percent confident that more than 3,000 person-days were lost to unexcused absences last year? Explain.