Making a Decision in Hypothesis Testing

Once you have formulated the null and alternate hypotheses, let’s turn our attention to the most important step of hypothesis testing — making the decision to either reject or fail to reject the null hypothesis — through an interesting example of a friend playing archery.

So, you learnt about what critical values are and how your decision to reject or fail to reject the null hypothesis is based on the critical values and the position of the sample mean on the distribution.

Let’s learn more about the critical region and understand how the position of the critical region changes with the different types of null and alternate hypotheses.

The formulation of the null and alternate hypotheses determines the type of the test and the position of the critical regions in the normal distribution.

You can tell the type of the test and the position of the critical region on the basis of the ‘sign’ in the alternate hypothesis.

       ≠ in H₁    →   Two-tailed test        →     Rejection region on both sides of distribution

       < in H₁    →   Lower-tailed test     →     Rejection region on left side of distribution

       > in H₁    →   Upper-tailed test     →     Rejection region on right side of distribution