In testing of hypothesis corresponding to a particular level of significance among all critical regions, ‘best critical region’ has

The 'best critical region' in hypothesis testing at a particular level of significance is the one that has the smallest probability of Type II error, or the highest power. This means it is the most effective at correctly rejecting a false null hypothesis.

Here are the steps to understand this:

1. In hypothesis testing, we start with a null hypothesis (H0) and an alternative hypothesis (H1). The null hypothesis is the statement being tested - often a statement of 'no effect' or 'no difference'. The alternative hypothesis is what we might believe if we find enough evidence against the null.

2. A critical region is the set of all values of the test statistic for which we would reject the null hypothesis. The level of significance (often denoted by alpha) is the probability of rejecting the null hypothesis when it is true - this is known as a Type I error.

3. However, there is another type of error, known as a Type II error, which is failing to reject the null hypothesis when it is false. The power of a test is the probability of correctly rejecting a false null hypothesis, or 1 minus the probability of a Type II error.

4. Therefore, among all critical regions corresponding to a particular level of significance, the 'best' one is the one that minimizes the probability of a Type II error, or equivalently, maximizes the power of the test. This is because it is the most effective at distinguishing between the null and alternative hypotheses when the null is false.