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

Answer: 1443

Step-by-step explanation:

Formula we use to find the sample size , if prior proportion is available :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

Given : Percent of the claims are covered : p= 60% =0.60

Margin of error : E=3% = 0.03

Critical value for 98 % confident : $z_{\alpha/2}=2.326$

Then , the required sample will be :

$n=(0.6)(1-0.6)(\dfrac{2.326}{0.03})^2=1442.74026667\approx1443$

Hence, the required sample size = 1443