Question

Define the alpha level and the critical region ans explain how they are related. Simply.

Answer 1

Alpha() level : -level is the probability of taking a wrong decision when the null hypothesis is true.Clearly

  -level is used in hypothesis tests and is called "level of significance". In such tests usually we take,=0.05,but 0.01 is also commonly used -levels.

-level can be controlled by the confidene interval. For an example: If we want 95% confidence interval, our -level would be 1-95%=1-0.95=0.05(for one tailed test) and 0.025 for two test tailed test.

Very clearly, -level is the probablity for a wrong decision for rejecting null hypothesis or we can say, Prob(Type I error)=.

So, one can say that, this  Prob(Type I error)= should be as small as possible.

Critical region:The critical region is the region of values that corresponds to the rejection of the null hypothesis at some chosen probability level.The critical value approach involves determining likely or unlikely by determining whether or not the observed test statistic is more extreme than would be expected if the null hypothesis were true. It entails comparing the observed test statistic to some cutoff value, called the "critical value." If the test statistic is more extreme than the critical value, then the null hypothesis is rejected in favor of the alternative hypothesis. If the test statistic is not as extreme as the critical value, then the null hypothesis is not rejected.

Some critical values are

chi square ,

standard normal,  

where 0.05 is the -level.