Chapter 8, Problem 58PS

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

Absenteeism: $\bar{X}=6.2\text{days,}S=7.3\text{days}\text{.}$

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:

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

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

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