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Answer: The analyst can reject the joint null hypothesis because the F-statistic is significant at the 95% confidence level.
## Explanation **C is correct.** The t-test would not be sufficient to test the joint null hypothesis. In order to test the joint null hypothesis, examine the F-statistic, which in this case is statistically significant at the 95% confidence level. Thus, the joint null hypothesis can be rejected. ### Key Points: - **Individual t-tests vs. Joint F-test**: The t-tests examine whether individual coefficients are significantly different from zero, while the F-test examines whether the entire set of coefficients (excluding the intercept) is jointly significant. - **P-values**: - β₁ p-value = 0.07 > 0.05 → Not individually significant at 95% confidence - β₂ p-value = 0.06 > 0.05 → Not individually significant at 95% confidence - F-statistic p-value = 0.045 < 0.05 → Jointly significant at 95% confidence - **Interpretation**: Even though neither coefficient is individually significant at the 95% level, the overall regression model is jointly significant, meaning the predictors together explain a significant portion of the variation in corporate revenue. A, B, and D are incorrect per the explanation for C above.
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For a sample of 400 firms, the relationship between corporate revenue (Y_i) and the average years of experience per employee (X_i) is modeled as follows:
An analyst wants to test the joint null hypothesis that and at the 95% confidence level. The p-value for the t-statistic for is 0.07, and the p-value for the t-statistic for is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct?
A
The analyst can reject the joint null hypothesis because each is different from 0 at the 95% confidence level.
B
The analyst cannot reject the joint null hypothesis because neither is different from 0 at the 95% confidence level.
C
The analyst can reject the joint null hypothesis because the F-statistic is significant at the 95% confidence level.
D
The analyst cannot reject the joint null hypothesis because the F-statistic is not significant at the 95% confidence level.