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 6 percent and have a confidence of 95.5 percent? (Round z values to 2 decimal places. Do not round other intermediate calculations. Round your final answer to the nearest whole number.) Number of observations

Answer 1

Solution:

Proportion(p) = 0.5

Margin of error = 0.06

Confidence interval = 95.5%

Alpha = 0.045

Alpha/2 = 0.0225

So zalpha/2 = 2.00

So margin of error for proportions can be calculated as

Margin of error = Zalpha/2*sqrt(p*(1-p)/n))

N = 2*2*0.5*0.5/(0.06*0.06) = 277.77 or 278