A researcher is testing the effectiveness of a skills mastery imagery program for soccer players. A sample of n = 25 college varsity players is selected and each player is tested on a ball-handling obstacle course before beginning the imagery program and again after completing the 5-week program. Of the 25 players, 18 showed improved performance on the obstacle course after the imagery program and 7 were worse.
a. Is this result sufficient to conclude that there is a significant change in performance following the imagery program? Use a two-tailed test with α = .05.
b. Because the outcome of the binomial test is a borderline z-score, use the real limits for X = 18 and verify that the entire z-score interval is located in the critical region.