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. Suppose slab avalanches studied in a region of Canada had an average thickness of %u03BC = 68 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).
59 51 76 38 65 54 49 62
68 55 64 67 63 74 65 79(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
x = 1 cm
s = 2 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 the region of Canada.
(a) What is the level of significance?
(b) What is the value of the sample test statistic?
(c) Find the P-value.