Final answer:
The p-value is a measure of evidence against the null hypothesis in a t test. It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.
Step-by-step explanation:
The p-value is a measure of the evidence against the null hypothesis in a t test. It represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true. In a t test, the p-value is calculated using a t distribution with n - 2 degrees of freedom. The p-value is the combined area in both tails of the distribution.
If the p-value is less than the chosen level of significance, typically 0.05, it indicates that the observed data provide strong evidence against the null hypothesis, and we reject the null hypothesis in favor of the alternative hypothesis. If the p-value is greater than or equal to the chosen level of significance, it suggests that there is insufficient evidence to reject the null hypothesis.
For example, if the p-value is 0.03, it means there is a 3% chance of obtaining the observed test statistic if the null hypothesis is true. This suggests strong evidence against the null hypothesis, assuming a significance level of 0.05.