Operations Management: Processes and Supply Chains, 12th Edition

Solved Problem 2

A library administrator wants to determine the proportion of time the circulation clerk is idle. The following information was gathered randomly by using work sampling:

Day	Number of Times Clerk Busy	Number of Times Clerk Idle	Total Number of Observations
Monday	8	2	10
Tuesday	7	1	8
Wednesday	9	3	12
Thursday	7	3	10
Friday	8	2	10
Saturday	6	4	10

If the administrator wants a 95 percent confidence level and a degree of precision of $\pm 4\text{ percent},$ how many more observations are needed?

Solution

The total number of observations made was 60. The clerk was observed to be idle 15 times. The initial estimate of the sample proportion is $\widehat{p}=15/60=\mathrm{0.25.}$ The required sample size for a precision of $\pm 4$ percent ...