Explanation:
When testing a joint null hypothesis, we should always examine the F-statistic. Bearing in mind that the p-value is the smallest level of significance at which we can reject the null hypothesis, the F-statistic is statistically significant at the 10% level. This means we can reject the null hypothesis. The t-statistic is not appropriate when testing a joint hypothesis. Rather, it’s used to test for the significance of individual regression coefficients. This means the t-statistics given in the question are not relevant for the task at hand.
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Q.74 A sample of 200 firms reveals the following relationship between the annual stock return (Yᵢ) and the average years of experience per employee, Xᵢ:
An analyst wishes to test the joint null hypothesis that β₁ = 0 and β₂ = 0 at the 10% level of significance. The p-value for the t-statistics of β₁ and β₂ are 0.12 and 0.11, respectively. The p-value for the F-statistic for the regression is 0.09. This implies that the analyst:
A
Can reject the null hypothesis since β₁ and β₂ are different from zero at the 10% level of significance.
B
Can reject the null hypothesis because the F-statistic is significant at the 10% level.
C
Cannot reject the null hypothesis because we have insufficient evidence to prove both β₁ and β₂ are different from zero at the 10% level of significance.
D
Cannot reject the null hypothesis because the F-statistic is not significant at the 10% level.