Question: Lake City has two shops, Zeke's and Elmer's, that handle the majority of the town's auto body repairs. Seven cars that were damaged in collisions were taken to both shops for written estimates of the repair costs. These estimates (in dollars) are shown in the following table.

Zeke's            1058         544          1349          1296          676          998           1698

Elmer's             995         540          1175          1350          605          970           1520

a. Construct a 99% confidence interval for the mean μd of the population paired differences, where a paired difference is equal to Zeke's estimate minus Elmer's estimate.

b. Test at the 5% significance level whether the mean μd of the population paired differences is different from zero. Assume that the population of paired differences is (approximately) normally distributed.