Final answer:
If a t-test yields a p-value less than 0.05, it suggests statistical significance, and the student can be more than 95% confident that the results are not due to chance, leading to the rejection of the null hypothesis.
Step-by-step explanation:
If a t-test produces a p-value that is less than 0.05, the student is more than 95% confident their results are NOT due to chance. When conducting a t-test, the p-value indicates the probability of observing the test result if the null hypothesis were true. An alpha level (or significance level), is commonly set at 0.05 or 5%, indicating the threshold for rejecting the null hypothesis. If the p-value is below this alpha level, the result is statistically significant, suggesting that the observed data is unlikely to have occurred by random chance and that there is evidence against the null hypothesis. Therefore, a p-value less than 0.05 means that there is less than a 5% chance the results occurred due to randomness, and correspondingly, the student can be more than 95% confident in the test's conclusion.
By setting an alpha at 0.05, findings with a p-value below this threshold are often considered 'statistically significant,' leading to the rejection of the null hypothesis. For example, if a t-test examining the average test scores from a sample yields a p-value of 0.0165, this is less than the alpha level of 0.05. Consequently, the decision would be to reject the null hypothesis, reinforcing the researcher's confidence that the experiment's findings reflect a true effect and are not just a product of chance.