Financial Risk Manager Part 1
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The estimated slope coefficient (β₁) for a certain stock is 0.8823 with a standard error equal to 0.0931. Assuming that the sample had 10 observations, carry out a statistical test to determine if the slope coefficient is statistically different than zero. Quote the test statistic and the decision rule using a 5% level of significance.
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TTanishq
A
9.477, reject H₀
B
9.477, do not reject H₀
C
2.307, reject H₀
D
2.307, do not reject H₀
Explanation:
Detailed Explanation
Hypothesis Formulation
- Null Hypothesis (H₀): β₁ = 0 (slope coefficient is not statistically different from zero)
- Alternative Hypothesis (Hₐ): β₁ ≠ 0 (slope coefficient is statistically different from zero)
Test Statistic Calculation
- Given: β₁ = 0.8823, standard error = 0.0931, n = 10 observations
- Degrees of freedom = n - 2 = 10 - 2 = 8
- Test statistic formula: t = (β₁ - β₀) / s.e.(β₁)
- t = (0.8823 - 0) / 0.0931 = 9.477
Critical Values
- For a 5% level of significance with a two-tailed test, α/2 = 0.025
- Critical t-value (t₀.₀₂₅,₈) = ±2.306 (from t-distribution table)
Decision Rule
- Rejection region: t < -2.306 or t > 2.306
- Non-rejection region: -2.306 ≤ t ≤ 2.306
Conclusion
- Since the calculated test statistic (9.477) > critical value (2.306), we reject the null hypothesis
- This means we have sufficient evidence to conclude that the slope coefficient is statistically different from zero at the 5% significance level
Therefore, the correct answer is 9.477, reject H₀
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