Answer: t-statistic

The correct statistic to calculate in order to test the hypothesis \( H_0: \beta = 1 \) against \( H_1: \beta \neq 1 \) is the t-statistic. The t-statistic is used to test hypotheses about a regression parameter in a linear regression model. It is calculated using the formula: \[ t = \frac{\beta_{\text{estimated}} - \beta_0}{\text{SE}(\text{estimated } \beta)} \] where: - \( \beta_{\text{estimated}} \) is the estimated beta value from the regression (0.86 in this case), - \( \beta_0 \) is the value of beta under the null hypothesis (1 in this case), - \( \text{SE}(\text{estimated } \beta) \) is the standard error of the estimated beta (0.80 in this case). Plugging in the values, the t-statistic is calculated as: \[ t = \frac{0.86 - 1}{0.80} = -0.175 \] Since the absolute value of the t-statistic (|t|) 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 at the 95% confidence level. The other options provided (Chi-squared test statistic, Jarque-Bera test statistic, and Sum of squared residuals) are not appropriate for this specific hypothesis test about a regression coefficient. The Chi-squared test is typically used for testing hypotheses about variances or proportions, the Jarque-Bera test is used to test for normality of residuals in a regression model, and the Sum of squared residuals is a measure of the fit of the regression model, not a test statistic for a hypothesis about a regression coefficient.

Author: LeetQuiz Editorial Team