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Answer: 9.477, reject H₀
## 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**
Author: Tanishq Prabhu
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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.
A
9.477, reject H₀
B
9.477, do not reject H₀
C
2.307, reject H₀
D
2.307, do not reject H₀