The marketing department at Insure-Me, a large insurance company, wants to advertise that customers can save, on average, more than $100 on their annual automotive insurance policies (relative to their closest competitor) by switching their policies to Insure-Me. However, to avoid potential litigation for false advertising, they select a random sample of 50 policyholders and compare their premiums to those of their closest competitor. A portion of the data is presented below.

Policyholder Competitor's Premium"Insure-Me" Premium

1...........................958................................1086

2..........................1034.................................366

⋮.............................⋮.......................................⋮

50........................1161.................................964

a. Specify the competing hypotheses to determine whether the mean difference between the competitor's premium and Insure-Me's premium is over $100.

b. Using the appropriate commands in Excel, find the value of the test statistic and the p-value.

c. What is the conclusion at the 5% significance level? What is the conclusion at the 10% significance level?