In hypothesis testing, what is rejected when the calculated t value exceeds the critical t value?

In hypothesis testing, what is rejected when the calculated t value exceeds the critical t value?

• A. Null Hypothesis
• B. Alternative Hypothesis
• C. P-value
• D. Confidence Interval

Answer: (A)

You compare the calculated t value to the cutoff provided by the critical t value from the t distribution for your chosen alpha and degrees of freedom. If the magnitude of the calculated t exceeds that cutoff, the result falls into the rejection region, meaning the observed data are unlikely if the null hypothesis is true. This is enough evidence to reject the null hypothesis and support the alternative hypothesis that there is an effect or difference. The p-value would correspondingly be smaller than the significance level in this situation, but the decision rule here centers on the t statistic crossing the critical threshold. The confidence interval represents a range of plausible values for the parameter and is not the direct mechanism for decision in this context, though a null value outside the interval would align with rejecting the null at that alpha level.

You compare the calculated t value to the cutoff provided by the critical t value from the t distribution for your chosen alpha and degrees of freedom. If the magnitude of the calculated t exceeds that cutoff, the result falls into the rejection region, meaning the observed data are unlikely if the null hypothesis is true. This is enough evidence to reject the null hypothesis and support the alternative hypothesis that there is an effect or difference. The p-value would correspondingly be smaller than the significance level in this situation, but the decision rule here centers on the t statistic crossing the critical threshold. The confidence interval represents a range of plausible values for the parameter and is not the direct mechanism for decision in this context, though a null value outside the interval would align with rejecting the null at that alpha level.