How does a critical t value of -1.96 impact the results of a hypothesis test?

A critical t value of -1.96 is specifically significant in the context of hypothesis testing, particularly when conducting a two-tailed test at the 0.05 significance level. This value serves as a threshold beyond which the null hypothesis can be rejected.

In a hypothesis test, the null hypothesis typically posits that there is no effect or no difference. If the calculated t statistic from sample data falls below the critical value of -1.96 or above 1.96 (in a two-tailed test), it indicates that the sample provides enough evidence to conclude that the observed effect is unlikely due to chance alone. As a result, this supports the possibility of a significant result, warranting the rejection of the null hypothesis in favor of the alternative hypothesis.

Understanding this relationship highlights the importance of the critical t value in determining the significance of the results, thus guiding researchers in interpreting their data accurately.