Question

Short answer

(A) We do not reject the null hypothesis, hence the value of ${\beta }_2=0$

(B) We reject the null hypothesis at 95% significance level, thus, the value of ${\beta }_2=0$

(C) Variable $X_2$might not be related to dependent variable y even if mathematically ${\hat{\mathbf{\beta }}}_{\mathbf{2}}\mathbf{>}{\hat{\mathbf{\beta }}}_{\mathbf{3}}$

Step-by-step solution

Step-by-Step Solution Step 1: Testing the significance of β2

Therefore, value of${\beta }_2=0$

Testing the significance of  β3

For, $\mathbf{\alpha }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{05}$the critical value of ${\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{025}}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{042}$ using the formulae table is ${\text{H}}_0$rejected if . $\left|\mathbf{t}\right|\mathbf{>}{\mathbf{t}}_{\mathbf{0}\mathbf{.}\mathbf{025}}$Since, 3.2068 > 2.042, we reject the null hypothesis at 95% significance level.

Therefore, value of ${\beta }_3$Is not equal to zero .

Predicting the model 

The null hypothesis $H_0;{\beta }_2=0$ is not rejected while the null hypothesis $H_0:{\beta }_3=0$ is rejected because the variable$X_2$ might not have a relationship with Y . The hypothesis testing implies that variable $X_2$ might not be predicting the overall model in a better way even if the mathematical value of coefficient of the variable calculated using the method of least square is higher than the other variable.