A sociologist is interested in studying the ability of teachers from low income

Question

A sociologist is interested in studying the ability of teachers from low income areas of major cities to cope with stress. Six schools were randomly chosen from low income areas and from each of these schools, five teachers were randomly chosen. The following table summarizes the average coping score (higher the score, the better the ability to cope) for each of these schools.

School 1 2 3 4 5 6

Mean 97 99 94 109 98 103 MSE=40

a. How much power does this study have if the true variances were such that 2? ^2 ? = ?^ 2 ? Please show hand calculations . b. In a random effects situation you can either increase a and/or n to increase the power. You investigate different combinations and find the following:

• a = 11, n = 5, 81.6% power

• a = 9, n = 6, 82.2% power

• a = 8, n = 7, 83.7% power

• a = 7, n = 8, 83.6% power

The largest difference between means is 4 units. Suppose that sigma^2=9. How large must n be (assuming balanced experiment, i.e., n_t=n)? Make sure you show your software inputs or hand calculations to receive full credits. Recall Exercise 5 in Lenture 9. There were a=6 randomly chosen schools each with n=5 reaches. How much power does this study have if the true variances were such that 2a^2,=a^2? Make sure you show your software inputs or hand calculations to receive full credits.

Explanation / Answer

a = 9, n = 6, 82.2% power

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