Question

e) Number of observations Number of units completed 610 14 A work sampling study was performed on four account executives in a stockbroker's office. Virtually all sales in the office are made through telephone solicitations. A total of 500 observations were made over a period of 1 week (7 hr/day, 5 days/week). The categories of activity and number of observations per category were as follows: (1) telephone calls, 164; (2) filing and sorting, 150; (3) reading and research, 101; (4) personal and nonproductive time, 85. Total sales during this period were $525,000, on which the office earned a com- mission of 4.0%. (a) Construct a 97% confidence interval on the proportion of time on the telephone during the 1-week period. (b) Estimate how many hours were spent on the phone by the four account executives during this period. (c)The office is considering hiring a clerk at $800/week to do the filing and sorting (category 2). This would reduce the time taken by the account executives on these activities by 7 hr/day. It is anticipated that all of these extra 7 hr would be spent on phone calls to increase sales. If sales level (in dollars) has been found to be proportional to time on the telephone, will the increase in commissions pay for the clerk? Compute the estimated net increase or decrease in weekly revenues from hir- ing the clerk.

Answer 1

1. Construct a 97% Confidence Interval for Telephone during one week Period

Z Value at 98.5% is 2.17, Total Observations is 500, Observations for Telephone Category is 164

So the population being 500 and proportion for telephone calls is 0.328 (164/500)

Hence the 97% confidence interval is

= (0.328) + 2.17*(0.328*0.672/500)^(1/2) = 0.3736

= (0.328) - 2.17*(0.328*0.672/500)^(1/2) = 0.28242.

2. Estimate how many hours were spent on Telephone Calls by four accounts executives

Total working hours contributed by four accounts executives is 140 Hours (7*5*4)

Contribution of Telephone Calls to Total Observations is 0.328 (164/500)

Estimated hours were spent on Telephone Calls by four accounts executives is 45.92 Hours (0.328*140)

3. Viability of Hiring a Clerk

Hours saved per week is 35 Hours (7 Hours*5 Days). Total hours spent on Telephone calls if the saved hours are utilised for Telephone Calls is 80.92 Hours (45.92+35)

Total Revenue through increase in the hours spent on Telephone Calls is $ 925,155 (525000*1.7622)

Proportionate Increase in the Commission through increase in the hours spent on Telephone Calls is $ 16,006.2 (525000*4%*0.7622)

It is viable to Hire a clerk at $ 800 / week.