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. 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):

i. Use a calculator with sample mean and sample standard deviation keys to verify that ‰ˆ 61.8 and s ‰ˆ 10.6 cm.
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.
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 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.
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 €œconservative€ answer.

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