Answer: t-statistic

## Explanation The correct test statistic to use in this scenario is the **t-statistic**. ### Why t-statistic? When testing hypotheses about individual regression coefficients in a linear regression model, the appropriate test statistic is the t-statistic. This is because: 1. **Single coefficient testing**: The hypothesis test is about a single regression coefficient (β = 1) 2. **Unknown population variance**: In regression analysis, the population variance is typically unknown 3. **Normal distribution assumption**: Under the classical linear regression assumptions, the estimated coefficients follow a t-distribution ### Calculation The t-statistic is calculated as: ``` t = (β_estimated - β_hypothesized) / SE(β_estimated) ``` Where: - β_estimated = 0.86 (the estimated coefficient from the regression) - β_hypothesized = 1 (the null hypothesis value) - SE(β_estimated) = 0.80 (standard error of the coefficient) ``` t = (0.86 - 1) / 0.80 = -0.175 ``` ### Why not the other options? - **B. Chi-squared test statistic**: Used for testing multiple restrictions or variance parameters, not individual coefficients - **C. Jarque-Bera test statistic**: Used for testing normality of residuals, not coefficient significance - **D. Sum of squared residuals**: A measure of model fit, not a test statistic for hypothesis testing ### Decision Rule With t = -0.175 and |t| < 1.96 (the critical value for a 95% confidence level), we cannot reject the null hypothesis that β = 1.

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