Chapter 11, Problem 9E

(a)

To determine

Whether the statement is correct or not and the reason for the same.

Answer to Problem 9E

Solution: The provided situation is incorrect because the hypothesis is tested using the slope coefficients of the regression equation. Hence, it should be:

$H_0:{\beta }_2=0$

Explanation of Solution

The provided situation is incorrect because the test statistic for the null hypothesis has been incorrectly recorded. The null and alternative hypotheses in the regression equation check the significance of the explanatory variables by equating their slope coefficients to zero versus not, or less than or more than zero. Hence, the null hypothesis should be written as

$H_0:{\beta }_2=0$

(b)

To determine

Whether the statement is correct or not and the reason for the same.

Answer to Problem 9E

Solution: The provided situation is incorrect because the $R^2$ is the multiple coefficient of correlation which gives the proportion of the variation in the response variable.

Explanation of Solution

The provided statement is incorrect. This is because $R^2$ is the multiple coefficient of correlation which explains the percent of variation in the response variable, as explained by the variation in the explanatory variables.

(c)

To determine

Whether the statement is correct or not and the reason for the same.

Answer to Problem 9E

Solution: The provided situation is incorrect because the meaning of p-value being too small is that it will be less than the significance level. Hence, the null hypothesis will be rejected implying that at least one of the explanatory variables differs from zero.

Explanation of Solution

The provided statement is incorrect. The p-value in ANOVA F-test does not mean that all the explanatory variables are significantly different from 0. This is because the null hypothesis in ANOVA states that one or more than one independent variables are equal to zero versus the alternative hypothesis that at least one of them significantly differs from zero. Hence, if the value of p-value is too small, it means that it will be less than the significance level. Hence, the null hypothesis will be rejected implying that at least one of the explanatory variables differs from zero.