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. Weather Station January April | 1 135 122 108 111 3 4 5 126 64 78 100 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use a - 0.01. (Let d= January - April.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Hg: Hg - 0; H: Mg < 0; left-tailed O Ho: Ma > 0; Hạ: My = 0; right-tailed O Hại Ha- 0; Hạ: Hg > 0; right-tailed O Hạ: Ha - 0; Hạ: My # 0; two-tailed (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately normal distribution. O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. O P-value > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005 < P-value < 0.025 O P-value < 0.005