In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f.

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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 three rats was given a reward ofone food pellet each time they ran a maze. A second group of threerats was given a reward of five food pellets each time they ran themaze. On day 2, the groups were reversed, so the first group nowgot five food pellets for running the maze and the second group gotonly one pellet for running the same maze. The average times inseconds for each rat to run the maze 30 times are shown in thefollowing table. Rat A B C D E F Time with one food pellet 3.6 4.33.1 3.1 3.5 3.9 Time with five food pellets 2.9 3.9 2.9 3.3 2.8 3.0Do these data indicate that rats receiving larger rewards tend torun the maze in less time? Use a 5% level of significance. (Let d =one − five.)
(a) What is the level of significance?
(b) What is the value of the sample test statistic? (Round youranswer to three decimal places.)