What is a critical value in hypothesis testing?

A critical value in hypothesis testing is a specific threshold that determines whether to reject the null hypothesis. It is derived from the sampling distribution of the test statistic, which is calculated based on the specific significance level (alpha) you have set for your test. If the computed test statistic falls beyond this critical value, it suggests that the observed data is statistically significant, leading to the rejection of the null hypothesis.

The critical value is essential because it defines the cutoff points on the distribution curve, delineating regions of acceptance and rejection for the null hypothesis. It essentially tells you when the evidence observed in your data is strong enough to conclude that there is a significant effect or difference, prompting you to reject the null hypothesis.

The other options do not accurately describe the role of a critical value in hypothesis testing: the mean of the sample data refers to a measure of central tendency, the proportion of a population is a parameter that can also be estimated but does not indicate a decision rule in hypothesis testing, and the average of two sample means pertains to comparing samples rather than establishing the threshold for rejecting a null hypothesis.