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.In an effort to determine if rats perform certain tasks morequickly if offered larger rewards, the following experiment wasperformed. On day 1, a group of four rats was given a reward of onefood pellet each time they climbed a ladder. A second group of fourrats was given a reward of five food pellets each time they climbeda ladder. On day 2, the groups were reversed, so the first groupnow got five food pellets for each climb and the second group gotonly one pellet for climbing the same ladder. The average times inseconds for each rat to climb the ladder 30 times are shown in thefollowing table. Rat A B C D E F G H Time 1 pellet 12.3 13.5 11.412.1 11.0 10.4 14.6 12.3 Time 5 pellets 11.1 12.4 12.2 10.6 11.510.5 12.9 11.0 Do these data indicate that rats receiving largerrewards tend to climb the ladder in less time? Use a 5% level ofsignificance. (Let d = Time 1 − Time 5.) (a) What is the level ofsignificance? State the null and alternate hypotheses. Will you usea left-tailed, right-tailed, or two-tailed test? H0: μd = 0; H1: μd< 0; left-tailed H0: μd = 0; H1: μd > 0; right-tailed H0: μd= 0; H1: μd ≠ 0; two-tailed H0: μd < 0; H1: μd = 0; left-tailed(b) What sampling distribution will you use? What assumptions areyou making? The standard normal. We assume that d has anapproximately uniform distribution. The standard normal. We assumethat d has an approximately normal distribution. The Student's t.We assume that d has an approximately normal distribution. TheStudent's t. We assume that d has an approximately uniformdistribution. What is the value of the sample test statistic?(Round your answer to three decimal places.) (c) Find (or estimate)the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050< P-value < 0.125 0.025 < P-value < 0.050 0.005