Which statement about the t-statistic’s use is true?

Which statement about the t-statistic’s use is true?

• A. It tests whether the sample mean equals the population mean
• B. It tests whether a b-value is significantly different from zero
• C. It tests whether the variance is large
• D. It tests whether two samples have equal variances

Answer: (B)

The t-statistic is used to determine whether a regression coefficient differs from zero. In a regression model, each coefficient (b) represents the expected change in the dependent variable for a one-unit change in its predictor, holding other variables constant. The t-statistic for that coefficient is calculated as the estimated value divided by its standard error, and under the null hypothesis that the true coefficient is zero, it follows a t distribution with the appropriate degrees of freedom. If the p-value is smaller than the chosen alpha level, we conclude that the predictor has a statistically significant effect, meaning the coefficient is not simply zero. This is why the statement about testing whether a b-value is significantly different from zero is the best description of the t-statistic’s use in this context. (Note: t-tests can test other things, like a mean against a target, in different contexts, but in regression, the primary use is evaluating whether coefficients differ from zero.)

The t-statistic is used to determine whether a regression coefficient differs from zero. In a regression model, each coefficient (b) represents the expected change in the dependent variable for a one-unit change in its predictor, holding other variables constant. The t-statistic for that coefficient is calculated as the estimated value divided by its standard error, and under the null hypothesis that the true coefficient is zero, it follows a t distribution with the appropriate degrees of freedom. If the p-value is smaller than the chosen alpha level, we conclude that the predictor has a statistically significant effect, meaning the coefficient is not simply zero. This is why the statement about testing whether a b-value is significantly different from zero is the best description of the t-statistic’s use in this context. (Note: t-tests can test other things, like a mean against a target, in different contexts, but in regression, the primary use is evaluating whether coefficients differ from zero.)