Please answer all three multiple choice questions below. Please include a brief reasoning of why you selected each answer.

1. The overall F-test obtained from performing a multi-way ANOVA comparing average cycling speed for 30 minutes of exercise across age groups (adolescents, adults, and the elderly) and geographic locations (rural and city subsamples) resulted in a p-value that was statistically significant for city versus rural but not for age. Which of the following is true?

a.The variability between the rural/city area groups is larger than variability within each area, however, the variability between age groups is the same.

b.The variability within the rural/city area groups is very large compared to between-group variability and the opposite for age.

c.The ratio of the between and within variability was not sufficiently large for rural/city area.

d.The F-statistic was larger than the critical value obtained from the F-distribution for age.

2.Which of the following statements regarding the odds ratio (OR) is false?

a.The OR cannot be a negative number.

b.If OR = 2.5 that means the odds in favor of the outcome for the group in the numerator is 2.5 times that of the group in the denominator.

c.OR = exp(logit) from a logistic regression model

d.If OR = 0, that means there are no differences between the two odds that are compared.

3.Which of the following statements is true?

a. ANOVA/ANCOVA and multiple linear regression are equivalent.

b. ANOVA/ANCOVA and multiple linear regression will generally yield very different results.

c. An interaction effect can only be tested between a continuous variable and a categorical variable.

d. An interaction effect can only be tested between two categorical variables.