Question

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, 7hr/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 the workers are idle. Assume that 200 observations were taken on each of the 10 workers, and members of the office pool were using the telephone in 590 of these observations. Phone records indicate that 3894 phone calls were made during the observation period.

A.  At the 95% confidence level, how many observations are required if the maximum error be no more than 5%? (z=2.33) Round up to integer number your answer.

B. Determine how many hours per day did an office pool spend on the telephone. Use 2 decimal places in the final answer.

C. What is the estimated average time per call?    Use 3 decimal places in the final answer.

with soln thank you!

Answer 1

Total No. of oberservations = 200 * 10 workers = 2000 observations
No. of observations in which telephone are used = 590 observations

= 590/2000 = 0.295

A)

For 95% confidence level,

z* = 1.96
Maximum error, c = 5% or 0.05

No. of observations, n is given by

n = 319.58 or 320 observations

B)

Total Time, TT = 22 days * 7 hours/day * 10 workers = 1540 hours

No. of hours per day an office pool spend on the telephone = * TT = 0.295 * 1540 = 454.30 hours

C)

No. of phone calls, Q = 3894 calls
Total Time, TT = 1540 hours
= 0.295

Estimated average time per call = () (TT)/ Q = (0.295)(1540)/ 3894 = 0.1667 hour per call = 0.1667 *60 mins per call = 7 mins per call