Question

(T/F) 1-8

1. The larger the P-value of a hypothesis test, the stronger the evidence against the null hypothesis.

2. In an ANOVA test comparing several population means, if the alternative hypothesis is true, the F statistic tends to be close to zero.

3. If the two variables in a two-way table are associated, the conditional distributions in the table are similar to each other.

4. In a multiple regression model, if the P-value associated with the F test is less than the significance level, we conclude that all explanatory variables in the model have a significant relationship with the response variable.

5. If multicollinearity is present, the standard errors of regression coefficient estimators tend to be large, i.e., the regression results are less precise.

6. The multiplication of two variables is used as a predictor if the two variables jointly affect the response. Group of answer choices

7. Even if the P-value of the F test in a multiple regression model is nearly zero, it is possible that the R² of the model is much less than one.

8. In selecting independent variables for a regression model, neither the forward selection method nor the backward elimination method guarantee the optimal combination of the independent variables.

9. For a given sample size, as the significance level increases, the probability of committing Type I error ____________ and the probability of committing the Type II error __________.

A. Increases, decreases

B. Increases, increases

C. Decreases, increases

D. Decreases, decreases

Answer 1

1. False - The larger the P-value of a hypothesis test, the stronger the evidence in favor the null hypothesis.

2. False - In an ANOVA test comparing several population means, if the alternative hypothesis is true, the F statistic tends to be close to high value.

3. False - If the two variables in a two-way table are independent, the conditional distributions in the table are similar to each other.

4. False - In a multiple regression model, if the P-value associated with the F test is less than the significance level, we conclude that at least one of the explanatory variables in the model have a significant relationship with the response variable.

5. True - If multicollinearity is present, the standard errors of regression coefficient estimators tend to be large, i.e., the regression results are less precise.

6. True - The multiplication of two variables is used as a predictor if the two variables jointly affect the response.

7. True - Even if the P-value of the F test in a multiple regression model is nearly zero, it is possible that the R² of the model is much less than one when the number of observations are large.

8. True - In selecting independent variables for a regression model, neither the forward selection method nor the backward elimination method guarantee the optimal combination of the independent variables.

9. For a given sample size, as the significance level increases, the probability of committing Type I error Increases and the probability of committing the Type II error decreases.

A. Increases, decreases