In this problem, 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. At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below.
Wilderness District 1 2 3 4 5
January 127 137 126 64 78
April 114 97 97 88 61
Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. Solve the problem using the critical region method of testing.