Final answer:
The correct statement that defines critical region and significance level is option a, with the critical region consisting of those values that lead to rejecting the null hypothesis, and the significance level being the probability of making a Type I error by incorrectly rejecting the true null hypothesis when using a predetermined alpha (α).
Step-by-step explanation:
The correct definition for a critical region and significance level is as follows:
- Critical region = those values for which we would reject the null hypothesis
- Significance level = the probability of incorrectly rejecting the null hypothesis
- Values that fall under the critical region correspond to significant values
The critical region is specifically the range of values in the results of a test that would lead us to reject the null hypothesis. The significance level is designated by the Greek letter alpha (α), and it represents the probability that we are making a Type I error, that is, the error of rejecting a true null hypothesis. Conventional levels of alpha are 5% (0.05), 1% (0.01), and so on. If a p-value is less than the chosen alpha, the result is said to be statistically significant, meaning it is unlikely to have occurred by chance under the null hypothesis, and we would reject the null hypothesis.
Method 1: Using the p-value, which is compared to the preset α to decide whether to reject the null hypothesis. Method 2: Using a table of critical values with a given significance level. In both methods, if the test statistic falls within the critical region, we reject the null hypothesis.