Insurance adjusters are always vigilant about being overcharged for accident repairs. The adjusters suspect that Repair Shop $1$quotes higher estimates than Repair Shop $2$. To check their suspicion,

the adjusters randomly select $12$cars that were recently involved in an accident and then take each of the cars to both repair shops to obtain separate estimates of the cost to fix the vehicle. The

estimates are given below in hundreds of dollars.

Assuming that the conditions for inference are reasonably met, which of the following significance tests could legitimately be used to determine whether the adjusters’ suspicion is correct?

I. A paired $t$test

II. A two-sample $t$test

III. A t test to see if the slope of the population regression line is $0$.

(a) I only

(b) II only

(c) I and III

(d) II and III

(e) I, II, and III

We are given that the adjusters suspect that Repair Shop $1$quotes higher estimates than Repair Shop $2$, to confirm their doubts, the adjusters randomly select $12$take each of the automobiles that were recently involved in an accident to both repair shops for independent quotes on the cost to repair the vehicle.

We need to find that tests that could legitimately be used to determine whether the adjusters’ suspicion is correct.

Here in this question , we will find tests that could legitimately be used to determine whether the adjusters' suspicion is correct. For that it is given that each observation is paired by car , so the$T$-test are paired.

We will treat given two population as not paired , we will do analysis then We will also note this thing that standard error will be quite on higher side . Generally , the two-sample$T$test are referenced when the observations are not paired.

For the third test , we will check if dummy variable slope related with the shop is$0$or not. Because we can possibly use dummy code the cars and shops.

So tests that could legitimately be used to determine whether the adjusters’ suspicion is correct are all the three tests.