In the following data pairs, A represents the cost of living index for housing and B represents the cost of living index for groceries. The data are paired by metropolitan areas in the United States. A random sample of 36 metropolitan areas gave the following information:

i. Let d be the random variable d = A - B. Use a calculator to verify that ‰ˆ 2.472 and sd ‰ˆ 12.124.
ii. Do the data indicate that the U.S. population mean cost of living index for housing is higher than that for groceries in these areas? Use α = 0.05.
Please provide the following information.
(a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
(b) What sampling distribution will you use? What assumptions are you making? Compute the value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)€“(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.
Assume that the distribution of differences is approximately normal.

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132 09 128 122 100 96 100 13 97 B: 125 18 139 104 103 07 109 117 105 120 115 98 11 93 97 110 92 110 09 105 09 104102 100 106 103 A 85 09 123 15 107 96 108 104 128 98 102 100 95 93 98 93 90 108 А: | 121 85 91 5 14 86 115 90 13 B: 102 96 92 108 17 109 107 100 95