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 ± $10. What is the minimum sample size n?
A)1083
B)4002
C)1537
D)2301

Question

Quizplus · Accepted Answer

We use the formula for the margin of error of a 95% confidence interval:
ME = 1.96 * sigma / sqrt(n)

We are given that ME <= $10 and sigma = $200. Plugging these values in and solving for n, we get:

10 = 1.96 * 200 / sqrt(n)
sqrt(n) = 1.96 * 200 / 10
n = (1.96 * 200 / 10)^2
n = 1537.6

Since n must be a whole number, we round up to get n = 1537. Therefore, the minimum sample size is 1537, which corresponds to choice C.

Ersatz Beneficial Insurance Wants to Estimate the Cost of Damage