The human resource (HR) director of a large corporation wishes to study absenteeism among its mid- level managers at its central office during the year. A random sample of 25 mid-level managers reveals the following:

• Absenteeism: X-bar = 6.2 days, S = 7.3 days.
• 13 mid- level managers cite stress as a cause of absence. 

a. Construct a 95% confidence interval estimate for the mean number of absences for mid- level managers during the year. 

b. Construct a 95% confidence interval estimate for the population proportion of mid-level managers who cite stress as a cause of absence. Suppose that the HR director wishes to administer a survey in one of its regional offices. Answer these questions: 

c. What sample size is needed to have 95% confidence in estimating the population mean absenteeism to within ± 1.5 days if the population standard deviation is estimated to be 8 days? 

d. How many mid- level managers need to be selected to have 90% confidence in estimating the population proportion of mid- level managers who cite stress as a cause of absence to within ± 0.075 if no previous estimate is available? 

e. Based on (c) and (d), what sample size is needed if a single survey is being conducted?