3.15 In a psychological experiment, the research question of interest is whether a rat ‘‘learned’’ its way through a maze during 64 trials.

Suppose the time-ordered observations on number of correct choices by the rat on each trial are as follows:

0, 1, 2, 1, 1, 2, 3, 2, 2, 2, 1, 1, 3, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 4, 3, 1, 2, 2, 1, 2, 2, 2, 2, 3, 2, 2, 3, 4, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 2, 3, 4, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 4, 4

(a) Test these data for randomness against the alternative of a tendency to cluster, using the dichotomizing criterion that 0, 1, or 2 correct choices indicate no learning, while 3 or 4 correct indicate some learning.

(b) Would the runs up and down test be appropriate for these data?

Why or why not?