In this problem, assume that the distribution of differences isapproximately normal. Note: For degrees of freedom d.f. not in theStudent's t table, use the closest d.f. that is smaller. In somesituations, this choice of d.f. may increase the P-value by a smallamount and therefore produce a slightly more \"conservative\" answer.At five weather stations on Trail Ridge Road in Rocky MountainNational Park, the peak wind gusts (in miles per hour) for Januaryand April are recorded below. Weather Station 1 2 3 4 5 January 139124 128 64 78 April 108 115 100 88 61 Does this informationindicate that the peak wind gusts are higher in January than inApril? Use α = 0.01. (Let d = January − April.) (a) What is thelevel of significance? State the null and alternate hypotheses.Will you use a left-tailed, right-tailed, or two-tailed test? H0:μd = 0; H1: μd ≠ 0; two-tailed H0: μd = 0; H1: μd < 0;left-tailed H0: μd > 0; H1: μd = 0; right-tailed H0: μd = 0; H1:μd > 0; right-tailed (b) What sampling distribution will youuse? What assumptions are you making? The Student's t. We assumethat d has an approximately uniform distribution. The Student's t.We assume that d has an approximately normal distribution. Thestandard normal. We assume that d has an approximately uniformdistribution. The standard normal. We assume that d has anapproximately normal distribution. What is the value of the sampletest statistic? (Round your answer to three decimal places.) (c)Find (or estimate) the P-value. P-value > 0.250 0.125