Financial Risk Manager Part 1

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:

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

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.