A clinical psychologist wished to compare three methods for reducing hostility levels in university students and used a certain test to measure the degree of hostility. A high score on the test indicated great hostility. The psychologist randomly selected 7 students for each treatment group. The data is summarized in the following table.

Method n_i y i .

1 7 86.75

2 7 81.57

3 7 73.00

The analysis of variance is given as follows:

Source DF SS MS F p-value

Treatment 2 812.357 406.179 4.764 0.001

Error 18 1534.681 85.26

Total 20 2347.038

(a) Write a linear contrast for the question: Is the mean test score for Method 1 different than the average of the mean test scores for Methods 2 and 3?

(b) Use Scheffes S Method to determine if the linear contrast in part (a) is significantly different from zero. = 0.05.