For Problems 9–21 assume that the distribution of differences d is moundshaped and symmetric.
Please provide the following information for Problems 9–21.
- (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) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the value of the sample test statistic and corresponding t value.
- (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) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
- (e) Interpret your conclusion in the context of the application.
In these problems, assume that the distribution of differences is approximately normal.
Note: For degrees of freedom d.f. not in the Student’s t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more “conservative” answer.
17. Economics: Cost of Living Index 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 (Reference: Statistical Abstract of the United States, 121st edition).
- i. Let d be the random variable d = A - B. Use a calculator to verify that d ≈ 2.472 and sd ≈ 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.
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Chapter 8 Solutions
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