Answer: The slope coefficient is statistically significant with a t-statistic of 2.03

## Explanation **Step 1: Set up the hypothesis test** - Null Hypothesis (H₀): b = 0 (slope coefficient is zero) - Alternative Hypothesis (H₁): b ≠ 0 (slope coefficient is different from zero) - This is a two-tailed test at 95% confidence level (α = 0.05) **Step 2: Calculate the t-statistic** The formula for the t-statistic is: $$ t = \frac{\hat{b} - b_0}{SE(\hat{b})} $$ Where: - $\hat{b}$ = estimated slope coefficient = 0.6 - $b_0$ = hypothesized value under null hypothesis = 0 - $SE(\hat{b})$ = standard error of slope coefficient = 0.2 $$ t = \frac{0.6 - 0}{0.2} = 3 $$ **Step 3: Determine the critical t-value** - Degrees of freedom = n - 2 = 36 - 2 = 34 - For a two-tailed test at 95% confidence level, α = 0.05, so α/2 = 0.025 in each tail - Critical t-value from t-distribution table: $t_{0.025, 34} = \pm 2.03$ **Step 4: Decision rule** - If |t-statistic| > critical t-value, reject the null hypothesis - Here: |3| > 2.03, so we reject H₀ **Step 5: Conclusion** The slope coefficient is statistically significant at the 95% confidence level with a t-statistic of 3, but the critical value for this test is 2.03. Therefore, the correct answer is option C, which correctly states that the slope coefficient is statistically significant with a critical t-statistic of 2.03. **Note:** While the calculated t-statistic is 3, option B is incorrect because it only states the calculated t-statistic without reference to the critical value. Option C correctly identifies both the statistical significance and the appropriate critical value for the test.

Author: Nikitesh Somanthe