Work Sampling

A work sampling study is to be performed on an office pool consisting of 10 persons to see how much time they spend on the telephone. The duration of the study is to be 22 days, seven hours per day. All calls are local. Using the phone is only one of the activities that members of the pool accomplish. The supervisor estimates that 25% of the time of the workers is spent on the phone.

Provide the following:

(a) At the 95% confidence level, how many observations are required if the lower and upper limits on the confidence interval are 0.20 and 0.30.

(b) Regardless of your answer to (a), suppose that 200 observations were taken on each of the ten workers (2000 observations total), and members of the office pool were using the telephone in 590 of these observations. Construct a 95% confidence interval for the true proportion of time on the telephone.

(c) Phone records indicate that 3894 phone calls (incoming and outgoing) were made during the observation period. What is the estimated average time per phone call?