Assumptions to consider. Thank you! s Potene about the high estimates they are r

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Assumptions to consider. Thank you! s Potene about the high estimates they are receiving tial insurance fraud? Insurance adjusters are concerned e. To see if the estimates are unrea- from Jocko's Garage. To seeitm ch of 10 damaged cars was taken to other garage and the estimates (in dollars) s an corded. Here are the results. OK 1410 1250 1550 1300 1250 Jockos Other 1300 900 950 10 1250 1200 Jockos Other 1520 1575 1750 3600 2250 2840 3380 2125 2600 1600 (a) For each car, subtract the estimate of the other garage standard deviation for this difference. from Jocko's estimate. Find the mean and the (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 sta- tistic 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 repay- ment 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

Explanation / Answer

(a)

(b) Null Hypothesis, H0: µD = 0

Alternate Hypothesis Ha: µD > 0

The test statistic, ts = (114-0) / (108.53/10) = 3.322

Number of degrees of freedom = 10-1 = 9

P-value = P (XD > 114) = P(t > (114-0) / (108.53/10)) = P(t >3.322) (with 9 degrees of freedom) = 0.0045

Using 0.05 significance level, since p-value < significance level, the p-value lies in the rejection region. We can reject the Null hypothesis and conclude that the strength of the evidence is good that Jocko’s shop is charging more on average than the other garage.

(c) The confidence interval is given as 114 ± tc x (108.53/10)

tc can be found using Excel function T.INV.2T(0.05,9) as 2.2622

The confidence interval is 114 - 2.2622 x (108.53/10) , 114 + 2.2622 x (108.53/10)

which after simplication is [36.362,191.638]

Since the value 0 is not contained in the confidence interval,we can conclude that indeed Jockos garage is charging more on average than the other garage.

(d) Looking at the confidence interval, we can conclude that Jocko's is charging at least $ 36.36 more than the other garages. So we can claim at least 1000 x 36.36 = $ 36,360 as repayment

Car Jocko's Other Difference 1 1410 1250 160 2 1550 1300 250 3 1250 1250 0 4 1300 1200 100 5 900 950 -50 6 1520 1575 -55 7 1750 1600 150 8 3600 3380 220 9 2250 2125 125 10 2840 2600 240 Mean 114 S.D. 108.53

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