3. To investigate whether online automobile insurance policies might be cheaper than the policies he can offer, a
local insurance agent compared the automobile insurance premiums for five of his customers with price quotations for the same coverage from online insurance companies. Results are shown in the table. Test the null hypothesis that the mean of the difference in premiums for all automobile policies is zero versus the relevant alternative, as indicated below. Use α = .01. Assume a normal distribution of differences. Policy Local Online 1 568 391 2 451 488 3 605 677 4 783 703 5 907 1008 State the null and alternative hypotheses for the test. State the correct formula for the test statistic. Justify your answer. (c) Construct the rejection region (d) Compute the value of the test statistic, and make a decision. (e) State a conclusion, in the context of the problem, about the mean of the difference in premiums for all policies, based on the test you performed.
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