Question

Ersatz Beneficial Insurance wants to estimate the cost of damage to cars due to accidents. The standard deviation of the cost is known to be $200. They want to estimate the mean cost using a 95 percent confidence interval within plus or minus $10. What is the minimum sample size n?

Answer

A. 1083
B. 4002
C. 1537
D. 2301

Answer 1

C. 1537

Explanation:

Standard deviation (s) = $200

For a 95 percent confidence interval, the value of 'z' is 1.960

The sample size (n) needed to assure that the sample mean cost of damage to cars due to accidents does not differ from the true mean by more than $10 is given by:

`10> z*(s)/(\sqrt n)\\\sqrt n>1.960*(200)/(10)\\n>1,536.64`

Rounding up to the next whole unit, the sample size needed is 1,537.