In testing of hypothesis corresponding to a particular level of significance among all critical regions, ‘best critical region’ has ans. least type I error least type II error greatest type I error greatest type II error

The 'best critical region' in hypothesis testing, corresponding to a particular level of significance among all critical regions, has the least Type II error.

Here's why:

In hypothesis testing, we have two types of errors: Type I and Type II.

Type I error occurs when we reject a true null hypothesis (also known as a "false positive"), and the level of significance, often denoted by alpha (α), is the probability of making a Type I error.

Type II error, on the other hand, occurs when we fail to reject a false null hypothesis (also known as a "false negative"). The probability of making a Type II error is often denoted by beta (β).

The 'best critical region' would be the one that minimizes these errors. However, there's a trade-off between Type I and Type II errors. If we decrease the probability of making a Type I error, we increase the probability of making a Type II error, and vice versa.

Given the options, the 'best critical region' would be the one with the least Type II error. This is because in many testing situations, a Type II error is considered more serious. For example, in a medical testing scenario, a Type II error could mean failing to detect a disease when it is actually present, which could have more serious consequences than a Type I error (detecting a disease when it is not actually present).