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.