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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. Suppose that 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 January 132 136 127 64 April 111 114 105 38 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use a = 0.01. Solve the problem using the critical region method of testing. (Le d = January - April. Round your answers to three decimal places.) test statistic = critical value = Interpret your conclusion in the context of the application. O Fail to reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. O Reject the null hypothesis, there is insufficient evidence to claim average peak wind gusts are higher in January. O Fail to reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. O Reject the null hypothesis, there is sufficient evidence to claim average peak wind gusts are higher in January. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? O We reject the null hypothesis using the P-value method, but fail to reject using the critical region method. O The conclusions obtained by using both methods are the same. O We reject the null hypothesis using the critical region method, but fail to reject using the P-value method