In a t-test, a small p-value indicates what?

In a t-test, a small p-value indicates what?

• A. Null hypothesis is true
• B. There is no significant difference
• C. There is a significant difference between means
• D. The test result is inconclusive

Answer: (C)

A small p-value means the observed difference between means is unlikely to occur if there is actually no difference. In a t-test, the p-value is the probability of getting results as extreme as what was observed under the assumption that the null hypothesis (no difference) is true. When this probability is small, we conclude that the data are inconsistent with no difference and, at the chosen significance level, we reject the null in favor of there being a statistically significant difference between the means. This does not prove the difference is large or practically important, nor does it prove the null is true in any absolute sense; it merely indicates statistical evidence against no difference.

A small p-value means the observed difference between means is unlikely to occur if there is actually no difference. In a t-test, the p-value is the probability of getting results as extreme as what was observed under the assumption that the null hypothesis (no difference) is true. When this probability is small, we conclude that the data are inconsistent with no difference and, at the chosen significance level, we reject the null in favor of there being a statistically significant difference between the means. This does not prove the difference is large or practically important, nor does it prove the null is true in any absolute sense; it merely indicates statistical evidence against no difference.