Answer: Can reject the null hypothesis because the F-statistic is significant at the 10% level of significance

## Explanation When testing a **joint null hypothesis** (β₁ = 0 AND β₂ = 0), we should use the **F-statistic** rather than individual t-statistics. Here's why: ### Key Points: 1. **Individual t-tests vs. Joint F-test**: - Individual t-tests examine each coefficient separately - F-test examines whether ALL coefficients in the model are jointly significant - For joint hypothesis testing, the F-test is appropriate 2. **P-value Interpretation**: - p-value = 0.09 for the F-statistic - Since 0.09 < 0.10 (10% significance level), we can reject the joint null hypothesis - The F-statistic is statistically significant at the 10% level 3. **Individual t-statistics**: - β₁ p-value = 0.12 (> 0.10) → not individually significant at 10% - β₂ p-value = 0.11 (> 0.10) → not individually significant at 10% - However, this doesn't matter for the joint hypothesis test ### Why Option B is Correct: - The F-statistic p-value (0.09) is less than the significance level (0.10) - This means we have sufficient evidence to reject the joint null hypothesis - The F-test properly accounts for testing multiple coefficients simultaneously ### Why Other Options are Incorrect: - **A**: Incorrect because individual t-statistics are not appropriate for joint hypothesis testing - **C**: Incorrect because the F-test provides sufficient evidence to reject the null - **D**: Incorrect because the F-statistic IS significant (p-value 0.09 < 0.10) ### Statistical Insight: The F-test for overall regression significance tests whether at least one of the coefficients is different from zero. Even if individual coefficients are not statistically significant, their joint effect might be significant due to correlation between variables or the combined explanatory power.

Author: Nikitesh Somanthe