a. Determine if the two independent samples analysis or paired analysis are appropriate to establish the difference between the following means:

• math test scores of 40 girls and 40 boys in some high school.
• math test scores of 40 male and female siblings, one brother and one sister from one family.
• math test scores of 50 parents and 50 children, one parent and one child from one family.
• math test scores of 50 adults born in 1960s and 50 adults born in 1980s.

b. Match the following measures of fit of a linear regression with their definitions/interpretations

1. Coefficient of determination (r-squared)

2. Standard error of estimate 3. P-value of F-test

1. Shows the percentage of variability of the dependent variable explained by the model (by the variability of all independent variables together) Shows the typical difference between the actual data and the predicted value for the dependent variable Shows whether the regression equation is significant or not at the given significance level (alpha)

2. Shows the percentage of variability of the dependent variable explained by the model (by the variability of all independent variables together) Shows the typical difference between the actual data and the predicted value for the dependent variable Shows whether the regression equation is significant or not at the given significance level (alpha)

3. Shows the percentage of variability of the dependent variable explained by the model (by the variability of all independent variables together) Shows the typical difference between the actual data and the predicted value for the dependent variable Shows whether the regression equation is significant or not at the given significance level (alpha)