In the context of hypothesis testing, what does a calculated t value of -3.39 compared to a critical t of -1.96 indicate?

In hypothesis testing, the comparison between the calculated t value and the critical t value is crucial for determining whether to reject or fail to reject the null hypothesis. A calculated t value of -3.39 indicates that the test statistic falls significantly beyond the threshold set by the critical t value of -1.96, which implies that the results are statistically significant.

The critical t value typically represents the cutoff point in the distribution beyond which the null hypothesis can be rejected. In this case, since -3.39 is much lower than -1.96, it indicates a stronger evidence against the null hypothesis. This suggests that the effect or difference being tested is not likely due to random chance, leading to the conclusion that the null hypothesis can be rejected.

Thus, the appropriate conclusion based on these t values is to reject the null hypothesis. This conclusion underscores the importance of understanding how calculated statistics relate to critical values in hypothesis testing, allowing analysts to make evidence-based decisions in clinical or research settings.