Question

A job in an insurance office involves telephone conversations with policyholders. The office manager estimates that about half of the employee’s time is spent on the telephone. How many observations are needed in a work sampling study to estimate that time percentage to within 7 percent and have a confidence of 98 percent? (Do not round intermediate calculations. Round your final answer to the nearest whole number.)

Answer 1

For 98% confidence level, the formula for determining sample size is following

where, S = desired relative accuracy = 7% (given)

p = percentage time spent on telephone = 50% (given)

q = percentage time idle = 1-p = 50%

N = Number of random observations needed (Sample size)

2.33 corresponds to 98% confidence level

Expressing the above equation to determine N, we get N = 2.332*pq / (Sp)2

Sp is the desired relative accuracy, p is a suffix here.

So the correct answer is 5.43*.5*.5/.07^2 = 277