In parts of the eastern United States, whitetail deer are a major nuisance to farmers and homeowners, frequently damaging crops, gardens, and landscaping. A consumer organization arranges a test of two of the leading deer repellents A and B on the market. Fifty-six unfenced gardens in areas having high concentrations of deer are used for the test. Twenty-nine gardens are chosen at random to receive repellent A, and the other 27 receive repellent B. For each of the 56 gardens, the time elapsed between application of the repellent and the appearance in the garden of the first deer is recorded. For repellent A, the mean time is 101 hours. For repellent B, the mean time is 92 hours. Assume that the two populations of elapsed times have normal distributions with population standard deviations of 15 and 10 hours, respectively.
a. Let µ1 and µ2 be the population means of elapsed times for the two repellents, respectively. Find the point estimate of µ1 – µ2.
b. Find a 97% confidence interval for µ1 – µ2.
c. Test at a 2% significance level whether the mean elapsed times for repellents A and B are different. Use both approaches, the critical-value and p-value, to perform this test.