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 three rats was given a reward of one food pellet each time they ran a maze. A second group of three rats was given a reward of five food pellets each time they ran the maze. On day 2, the groups were reversed, so the first group now got five food pellets for running the maze and the second group got only one pellet for running the same maze. The average times in seconds for each rat to run the maze 30 times are shown in the following table.

Rat	A	B	C	D	E	F
Time with one food pellet	3.6	4.1	2.9	3.1	3.5	3.9
Time with five food pellets	2.9	3.5	3.0	3.3	2.8	3.0

Do these data indicate that rats receiving larger rewards tend to run the maze in less time? Use a 10% level of significance. (Let d = one − five.)

(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?

(b) What sampling distribution will you use? What assumptions are you making?

What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

(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?

(e) State your conclusion in the context of the application.

Answer 1