How is the rejection region defined?
The rejection region is the region that represents the set of values in a test statistics whereby the null hypothesis is rejected (Park, 2015) . This region is also called critical region. It is the one that leads us to reject the null hypothesis. In case the test statistics fall into the rejection region, then, we reject the null hypothesis in favour of the alternative hypothesis.
Acceptance region
Rejection region (0.05%) 95% (0.05%) Rejection region
How is that related to the p value?
P-value refers to the probability of obtaining an effect which is either equal to or more than the observed value putting into consideration that the null hypothesis is true. The measurement can refer to difference in measurements between two variables. In other words, the calculated probability, which is also referred to as p-value is the probability of finding the observed or even more extreme results when the null hypothesis of the study is true (Harrell,2015) . It is also understandable that when defining the term ‘extreme’, it depends on the way we are testing the hypothesis. In fact, it can be described in terms of rejecting H o in case it is true in actual sense,hence,1-p value is equal to the rejection region, meaning, both p value and rejection region are inversely related.
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When do you reject or fail to reject the null hypothesis?
We reject the null hypothesis through the analysis in case the alternative hypothesis is correct. On the other hand, we fail to reject the null hypothesis through the analysis if the null hypothesis is correct or accurate.
Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?
Statisticians can be requested to complete the hypothesis testing under various circumstances, for instance, in medicine; it can be utilized to test whether the treatment of a certain type of drug is effective. Assume a company is developing a medication for lowering blood pressure. They can, for instance carry out a study whereby a group receives the new medication invented and the other one receives a placebo. Blood pressure can then be collected for each of the groups. Then, statisticians can now come in to analyze the data using hypothesizes testing to know whether the treatment was effective. If the researcher wants to know whether the group average blood pressure is less than group under control, In this case, the null and alternative hypothesis can be
Null hypothesis drug =u control
Alternative hypothesis drug u control
In this case u drug represents average blood pressure of group of treatment u control representing blood pressure of control group.
The p-value is then calculated such that in case it falls below a certain threshold, the null hypothesis can then be rejected.
References
Harrell, F. E. (2015). Introduction. In Regression Modeling Strategies (pp. 1-11). Springer, Cham.
Park, H. M. (2015). Hypothesis testing and statistical power of a test.
