7.40 Potential insurance fraud? Insurance adjusters are concerned about the high estimates they are receiving from Jocko’s Garage. To see if the estimates are unreasonably high, each of 10 damaged cars was taken to Jocko’s and to another garage and the estimates (in dollars) were recorded. Here are the results:
| Car | 1 | 2 | 3 | 4 | 5 |
| Jocko’s | 1410 | 1550 | 1250 | 1300 | 900 |
| Other | 1250 | 1300 | 1250 | 1200 | 950 |
| Car | 6 | 7 | 8 | 9 | 10 |
| Jocko’s | 1520 | 1750 | 3600 | 2250 | 2840 |
| Other | 1575 | 1600 | 3380 | 2125 | 2600 |
(a) For each car, subtract the estimate of the other garage from Jocko’s estimate. Find the mean and the standard deviation for this difference.
(b) Test the null hypothesis that there is no difference between the estimates of the two garages. Be sure to specify the null and alternative hypotheses, the test statistic with degrees of freedom, and the P-value. What do you conclude using the 0.05 significance level?
(c) Construct a 95% confidence interval for the difference in estimates.
(d) The insurance company is considering seeking repayment from 1000 claims filed with Jocko’s last year. Using your answer to part (c), what repayment would you recommend the insurance company seek? Explain your answer.