The following data are based on information from the Regis University Psychology Department. 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 ­one food pellets each time they ran the maze. On day 2, the groups were reversed, so the ­first group now got ­one 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.

Do these data indicate that rats receiving larger rewards tend to run the maze in less time? Use a 5% level of signi­ficance.

(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? Compute the value of the sample test statistic and corresponding t value.

(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.

(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 a?

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

Rat Time with one food pellet Time with tive tood pellets 3.6 3.1 3.5 3.9 4.2 3.7 2.9 3.0 3.0 3.3 2.8 3.0