Question

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. In an effort to determine if rats perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day 1, a group of four rats was given a reward of one food pellet each time they climbed a ladder. A second group of four rats was given a reward of five food pellets each time they climbed a ladder. On day 2, the groups were reversed, so the first group now got five food pellets for each climb and the second group got only one pellet for climbing the same ladder. The average times in seconds for each rat to climb the ladder 30 times are shown in the following table. Rat A B C D E F G H Time 1 pellet 12.3 13.5 11.4 12.1 11.0 10.4 14.6 12.3 Time 5 pellets 11.1 12.4 12.2 10.6 11.5 10.5 12.9 11.0 Do these data indicate that rats receiving larger rewards tend to climb the ladder in less time? Use a 5% level of significance. (Let d = Time 1 − Time 5.) (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? 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 are you making? The standard normal. We assume that d has an approximately uniform distribution. The standard normal. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately normal distribution. The Student's t. 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. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. Fail to reject the null hypothesis, there is insufficient evidence to claim that the mean time for rats receiving larger rewards to climb the ladder is less. Reject the null hypothesis, there is insufficient evidence to claim that the mean time for rats receiving larger rewards to climb the ladder is less. Reject the null hypothesis, there is sufficient evidence to claim that the mean time for rats receiving larger rewards to climb the ladder is less. Fail to reject the null hypothesis, there is sufficient evidence to claim that the mean time for rats receiving larger rewards to climb the ladder is less.

Answer 1