When only two treatments are involved, ANOVA and the Student t test (Chapter 11) result in the same conclusions. Also, t2 = F. As an example, suppose that 14 randomly selected students were divided into two groups, one consisting of 6 students and the other of 8. One group was taught using a combination of lecture and programmed instruction, the other using a combination of lecture and television. At the end of the course, each group was given a 50-item test. The following is a list of the number correct for each of the two groups. Using analysis of variance techniques, test the null hypothesis, H0 that the two mean test scores are equal.

Lecture and Programmed Instruction Lecture and Television
12 37
15 23
26 33
22 24
12 27
13 29
25
25

a. Complete the ANOVA table (2 decimal places)
Source SS df MS F
Factor
Error
Total

b. Using aσ = 0.1 level of significance, compute the test statistic F:

c. Using the t-test from Chapter 11, compute t.

d. Is there a difference in the test results from the two groups?

e. Is t2 ≈ F?