Refer to Exercise 9.1. Analyze these same data using the paired t test. Compare your resul...

Refer to Exercise 9.1. Analyze these same data using the paired t test. Compare your results to the results from Exercise 9.1. (The F test for testing treatment differences in a randomized complete block design when there are only two treatments is equivalent to the paired t test of Chapter 6. This can be shown by noting that t2 = F, where F is the F test for treatment differences.)

Exercise 9.1

A researcher wanted to determine whether attending a Head Start program improves the academic performance of first graders from a low-income community. The researcher obtained a random sample of six children who attended a Head Start program and six who did not. There were large differences in the type of support the students received at home from their parents. Thus, after assessing the home environment of the twelve students, the researcher paired the students based on the similarities in their home environment. After completing the first grade, the students were given an overall aptitude examination. The results are shown here.

a. Do the students who attended a Head Start program appear to have higher mean aptitude scores than the students who did not attend such a program? Use α = .05.

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b. Give the efficiency of the randomized complete block design relative to a completely randomized design. Interpret your findings.