Chapter 8.2, Problem 19P

Please provide the following information for Problems 11–22.

1. (a) What is the level of significance? State the null and alternate hypotheses.
2. (b) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the appropriate sampling distribution value of the sample test statistic.
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 given 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.

19. Ski Patrol: Avalanches Snow avalanches can be a real problem for travelers in the western United States and Canada. A very common type of avalanche is called the slab avalanche. These have been studied extensively by David McClung, a professor of civil engineering at the University of British Columbia. Slab avalanches studied in Canada have an average thickness of μ = 67 cm (Source: Avalanche Handbook by D. McClung and P. Schaerer). The ski patrol at Vail, Colorado, is studying slab avalanches in its region. A random sample of avalanches in spring gave the following thicknesses (in cm):

1. i. Use a calculator with mean and standard deviation keys to verify that $\bar{x}\approx \text{61}.\text{8}$ and s ≈ 10.6 cm.
2. ii. Assume the slab thickness has an approximately normal distribution. Use a 1% level of significance to test the claim that the mean slab thickness in the Vail region is different from that in Canada.