Question

2) In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at a local bank take per year. Based on earlier studies it is known that the standard deviation is 12.3 days per year. How large a sample must be selected if the company wants to be 95% confident that their estimate is within 3 days of the true mean?

Answer 1

Solution

standard deviation =   =12.3

Margin of error = E = 3

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96* 12.3 / 3 )2

n =64.57

Sample size = n =65