Question

A car insurance company would like to determine the proportion of accident claims covered by the company. According to a preliminary estimate, 60 percent of the claims are covered. How large a sample should be taken to estimate the proportion of accident claims covered by the company if we want to be 98 percent confident that the sample percentage is within ±3 percent of the actual percentage of the accidents covered by the insurance company?

Answer 1

Solution :

Given that,

= 60%=0.60

1 - = 1 - 0.60 = 0.40

margin of error = E = 3% = 0.03

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

Sample size = n = (Z_/2 / E)² * * (1 - )

= (2.326 / 0.03)² * 0.60 * 0.40

= 1442.74

Sample size = 1443 (rounded)