Final answer:
The p-value in hypothesis testing measures the probability of observing a test statistic as extreme as the sample result, assuming the null hypothesis is true. A very small p-value indicates strong evidence against the null hypothesis, often leading to its rejection. The p-value is commonly used with a significance level like 0.05 to make decisions in statistical tests.
Step-by-step explanation:
The p-value measures the probability that an event will happen purely by chance, assuming the null hypothesis is true. If the p-value is very small, it indicates that the observed test statistic is very unlikely to occur if the null hypothesis is true. This provides significant evidence to suggest that the null hypothesis may be false, leading to its rejection in favor of the alternative hypothesis.
For example, in hypothesis testing, we often use a significance level (alpha) of 0.05 or 0.01. If the p-value is less than the chosen alpha level, we reject the null hypothesis. This decision suggests that there is a statistically significant effect or difference.
Moreover, the p-value can be used in various statistical tests like t-tests and correlation coefficient tests. When using technology like statistical software or calculators, the p-value can be computed directly, often through functions like LinRegTTest for linear regression analysis. An example of interpreting a p-value from LinRegTTest could be: if the p-value is 0.026, which is less than the significance level of 0.05, the null hypothesis is rejected, indicating a significant linear relationship between two variables.