Question

In hypothesis testing, what is the critical value?

1) The value that separates the critical region from the non-critical region
2) The value that determines the level of significance
3) The value that determines the power of the test
4) The value that determines the sample size

Answer 1

In hypothesis testing, the critical value is the value that separates the critical region from the non-critical region

Step-by-step explanation:

The critical value in hypothesis testing is the point that delineates the critical region from the non-critical region, and it plays a pivotal role in deciding whether to reject the null hypothesis.

Essentially, it is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the test statistic falls within the critical region (beyond the critical value), the null hypothesis is rejected.

There are different types of tests, such as left-tailed, right-tailed, and two-tailed tests, which correspond to the directions in which one can reject the null hypothesis based on the alternative hypothesis (Ha). The type of test determines where the critical regions are located in the distribution. A smaller p-value, such as 0.001, indicates that there is stronger evidence against the null hypothesis than a larger p-value, like 0.04.

To make a conclusion in hypothesis testing, one can use either the p-value compared to the significance level (alpha, α) or a table of critical values at a given α. Commonly, a significance level of 0.05 is used if not specified otherwise.