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. 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: \[ t = \frac{\text{estimated } \beta - \text{hypothesized } \beta}{\text{standard error of the estimated } \beta} \] In this case, the estimated beta (\( \hat{\beta} \)) is 0.86, the hypothesized beta (\( \beta_0 \)) is 1, and the standard error of the estimated beta (\( SE(\hat{\beta}) \)) is 0.80. Plugging these values into the formula gives: \[ t = \frac{0.86 - 1}{0.80} = -0.175 \] Since the absolute value of the calculated 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 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.

Author: LeetQuiz Editorial Team