A clinical psychologist wished to compare three methods for reducing hostility levels in university students. A psychological test (HLT) was used to measure the degree of hostility. High scores on this test indicate great hostility. Eleven students obtaining high and nearly equal scores were used in the experiment. Five were selected at random from among the 11 problem cases and treated by method A. Three were taken at random from the remaining 6 students and treated by method B. The other 3 students were treated by method C. All treatments continued throughout a semester. Each student was given the HLT test again at the end of the semester, with the results shown in the accompanying table.
| Method A |
Method B |
Method C |
| 73 |
54 |
79 |
| 83 |
74 |
95 |
| 76 |
71 |
87 |
| 68 |
|
|
| 80 |
|
|
a. Do the data provide sufficient evidence to indicate that at least one of the methods of treatment produces a mean student response different from the other methods? Give bounds for the attained significance level.
b. Applet Exercise Find the exact p-value by using the applet F-Ratio Probabilities and Quantiles.
c. What would you conclude at the α =.05 level of significance?