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 bar = 9.7 days, S = 4.0 days
• 12 clerical workers were absent more than 10 days.
a) Construct a 95% confidence interval estimate of the mean number of absences for clerical workers during the year.
b) Construct a 95% confidence interval estimate of the population proportion of clerical workers absent more than 10 days during the year.
Suppose, that the personnel director also wishes to 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 if being conducted?