Question

Car insurance companies want to keep track of the average cost per claim. The current data in use for Auto Insurance R Us is an average of $2,200 for each claim with a standard deviation of $500. With this average, the company can stay competitive with rates but not lose money. However, the statistician for the company believes that the cost of the average claim has increased. He pulled 40 recent claims and found the average to be $2,350.

Which most restrictive level of significance would suggest that the company should raise rates?
1%
2.5%
5%
10%

Answer 1

I just took the test, the answer is 5%.

Answer 2

10%

Explanation:

Given that Car insurance companies want to keep track of the average cost per claim. The current data in use for Auto Insurance R Us is an average of $2,200 for each claim with a standard deviation of $500.

Sample mean = 2350 and sample size n =40

Std error of sample = std ddviation/sqrt of n

=
`(500)/(√(40) ) \\=79.06`

Margin of error at 95%=1.96*79.06

=154.95

Margin of error at 90%=1.645*79.06 =129

Mean difference =2350-2200=150>margin of error for 129

Hence for 10%it should raise rates