The test scores for three randomly selected samples of five students who took a course with three different instructors are shown in Table 1.
Table 1: Test Scores:
|
Students
|
TEACHER 1
|
TEACHER 2
|
TEACHER 3
|
|
1
|
90
|
85
|
83
|
|
2
|
55
|
90
|
60
|
|
3
|
84
|
90
|
80
|
|
4
|
91
|
95
|
85
|
|
5
|
85
|
80
|
71
|
|
|
|
|
(a) For α = 0.05, test whether there is a significant difference among the average score of the three samples of students. Specifically:
(i) State your null and alternative hypothesis.
(ii) Calculate the value of the test statistic showing all the steps. That is, calculate x¯¯, SST R,MST R, SSE, MSE and the value of your F test.
(iii) Indicate what is the critical value associated with your test statistic and how you find it in the tables.
(iv) State the conclusion of your test and provide an interpretation of your result.