The personnel director of a large corporation wishes to study absenteeism among clerical workers at the corporation's central office during the year. A random sample of 25 clerical workers reveals the following:
• Absenteeism: X = 9.7 days, S = 4.0 days.
• 12 clerical workers were absent more than 10 days.
a. Construct a 95% confidence interval estimate for the mean number of absences for clerical workers during the year.
b. Construct a 95% confidence interval estimate for the population proportion of clerical workers absent more than 10 days during the year.
Suppose that the personnel director also wishes to take a survey in a branch office. 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 4.5 days?
d. How many clerical workers need to be selected to have 90% confidence in estimating the population proportion 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?