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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 Television12 3715 2326 3322 2412 2713 29 25 25
a. Complete the ANOVA table (2 decimal places)Source SS df MS FFactor 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?
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