The personnel director of a large corporation wants to study absenteeism among
clerical workers at the corporation's central office during the year. A random
sample of 35 clerical workers reveals the following: 

? Absenteeism: = 10.7 days, S = 3.0 days.
12 clerical workers were absent more than 10 days.

a. Set up a 99 % confidence interval estimate of the average number of absences for clerical workers last year.

b. Set up a 99% confidence interval estimate of the population proportion of clerical workers absent more than 10 days last year.

c. If the personnel director also wants to take a survey in a branch office, what sample size is needed if the director wants to be 80% confident of being correct to within ? 1.8 days and the population standard deviation is assumed to be 4.8 days?

d. If the personnel director also wants to take a survey in a branch office, what sample size is needed if the director wants to be 80% confident of being correct to within ? 0.075 of the population proportion of workers who are absent more than 10 days if no previous estimate is available?