In hypothesis testing, what role does the test statistic play?

The test statistic plays a crucial role in hypothesis testing by summarizing sample data and providing a basis for making decisions about the null and alternative hypotheses. When conducting a hypothesis test, researchers collect sample data and calculate a test statistic that reflects how far the sample statistic deviates from what would be expected under the null hypothesis. This statistic is then compared to a critical value or interpreted in the context of a p-value to determine whether the evidence is strong enough to reject the null hypothesis in favor of the alternative.

By condensing the sample data into a single numerical value, the test statistic effectively allows researchers to assess the likelihood of observing the sample data if the null hypothesis were true. Thus, it is a fundamental component that aids in the decision-making process regarding the hypotheses.