1. A family sociologist is interested in the difference in marital satisfaction between working and nonworking wives. Using a standardized marital satisfaction inventory with a standard deviation (σ) of 25, determine the power of the test of the null hypothesis H0: μi - μ2 = 0 under the following conditions:

a. For ni = n2 = 75, the standard error of the difference is

For α = .05, determine the power for both a one-tailed and a two-tailed test of the null hypothesis H0: μi - μ2 = 0 against the alternative hypothesis Hα: μi - μ2 = 7.5 (the effect size equals 7.5).

b. For effect size equal to 7.5 and a one-tailed test, determine the power for α= .01 and α = .10.

c. Now let n1 = n2 = 120; determine the standard error of the difference, and determine the power of a one-tailed test for α = .05 and ES = 5.0.

d. Now for the original study, in which n1 = n2 = 75, let the effect size equal 3.5. Find the power of a one-tailed test at α = .05.

2. The president of a major educational foundation is investigating the average salary of faculty members in major state universities across the United States He decides to test the null hypothesis H0:μ = 24,500 and is concerned with making a Type II error only if the average salary is less than $600 above this hypothesized value. In this case, the effect size is set at 600; the alternative hypothesis is Hα :μ = 25,100. Assume that the population standard deviation (σ) equals $4,800.

3. In Exercise 1, the president of the educational foundation was testing the null hypothesis H0:μ = 24.500. Using σ = 4,800, determine the appropriate sample size given the following conditions. Check your answers with Table C.11. 

a. α = .05, β = .20, ES = 600, one-tailed and two-tailed tests. 

b. α = .05, β = .20, ES = 1,200, one-tailed test only. 

c. α = .01, β = .05, ES = 600, one-tailed and two-tailed tests. 

d. α = .01, β = .05, ES = 1,200, one-tailed test only.