Insurance adjusters are always concerned 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 in hundreds of dollars.

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

a. A paired$t$ test

b. A two-sample $t$test

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

d. A chi-square test for homogeneity

e. A chi-square test for goodness of fit

Given in the question that, insurance adjusters are always concerned 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 in hundreds of dollars.

We need to find significance tests used to determine whether the adjusters’ suspicion is correct if the conditions for inference are met .

We're going to assume that all of the prerequisites have been met. The estimates are listed in the question's table. We should notice that each car has two data values: the estimate from repair shop$1$and the estimate from repair shop$2$. This means that the samples are dependent and that the data is paired because the data is presented in pairs, each pair consisting of two estimates for the same vehicle. Because the data is paired, a paired t test is the best option. As a result, option (a) is the proper choice.