Refer to Practice Exercise 2. (a) Groups 1 and 2 are related, as are Groups 3 and 4. Construct and test a contrast that will compare the average of the means for Groups 1 and 2 with that for Groups 3...

Refer to Practice Exercise 2.

(a) Groups 1 and 2 are related, as are Groups 3 and 4. Construct and test a contrast that will compare the average of the means for Groups 1 and 2 with that for Groups 3 and 4. Assign a p value for this test assuming that this contrast was planned in advance and is the only contrast that will be tested.

(b) Assign a p value (or construct a critical region) for the test in part (a), assuming that the contrast was decided after examining the sample means. What conclusion do you reach?

Exercise 2

An experiment has four factor levels. Each group had a sample size of five. Table 6.21 shows the sample means and standard deviations both within the groups and for the overall sample.

Construct the ANOVA table for this data, and test the hypothesis that there are no differences in the population group means.