Chapter 8, Problem 5CRP

Before you solve each problem below, first categorize it by answering the following question: Are we testing a single mean, a difference of means, a paired difference, a single proportion, or a difference of proportions? Assume underlying population distributions are mound-shaped and symmetric for problems with small samples that involve testing a mean or difference of means. Then provide the following information for Problems 5–18.

1. (a) What is the level of significance? State the null and alternate hypotheses.
2. (b) Check Requirements What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic and corresponding distribution value.
3. (c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
4. (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 α?
5. (e) Interpret your conclusion in the context of the application.

   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. Answers may vary due to rounding.

5. Vehicles: Mileage Based on information in Statistical Abstract of the United States (116th edition), the average annual miles driven per vehicle in the United States is 11.1 thousand miles, with σ ≈ 600 miles. Suppose that a random sample of 36 vehicles owned by residents of Chicago showed that the average mileage driven last year was 10.8 thousand miles. Does this indicate that the average miles driven per vehicle in Chicago is different from (higher or lower than) the national average? Use a 0.05 level of significance.