
Explanation:
The correct statistic to calculate in order to test the hypothesis against is the t-statistic. This is because the t-statistic is used to test hypotheses about regression parameters in a linear regression model. The t-statistic is calculated using the formula:
In this case, the estimated beta () is 0.86, the hypothesized beta () is 1, and the standard error of the estimated beta () is 0.80. Plugging these values into the formula gives:
Since the absolute value of the calculated t-statistic () is less than the critical value of 1.96 (which corresponds to a 95% confidence level for a two-tailed test), we cannot reject the null hypothesis. This means that there is not enough evidence to conclude that the beta of stock CDM is different from 1 based on the given data and test. The other options provided (Chi-squared test statistic, Jarque-Bera test statistic, and Sum of squared residuals) are not appropriate for testing a hypothesis about a regression coefficient in this context.
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In the context of hypothesis testing concerning the parameter β in a linear regression model, if we are to test the null hypothesis H0: β = 1 against the alternative hypothesis Ha: β ≠ 1, which specific test statistic should be calculated to evaluate this hypothesis?
A
t-statistic
B
Chi-squared test statistic
C
Jarque-Bera test statistic
D
Sum of squared residuals
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