What does a high t value indicate?

A high t value in the context of hypothesis testing, particularly in t-tests, indicates a significant difference between the means of the groups being compared. When conducting a t-test, the t value is calculated from the data, reflecting the ratio of the difference between group means to the variability of the data. A high t value suggests that the difference observed is greater than what might be expected due to random variation alone. In other words, it provides evidence against the null hypothesis, which typically states that there is no difference between the groups. Therefore, a high t value increases the likelihood of concluding that the groups are indeed significantly different from one another, supporting option B.

In contrast, the other options do not accurately represent what a high t value implies. A low t value, rather than a high one, would typically suggest that the groups do not differ significantly, indicating option A is incorrect. Risk of random error is associated with the variability in data, not directly indicated by a high t value (option C). Finally, the sample size affects the t value but a high t value does not inherently indicate that the sample size is small (option D). Thus, a high t value solidly suggests a significant difference between the group means.