Question

why is it important to understand the difference between a one tailed and two tailed test

Answer 1

Solution :

We decide the tail of the test based on the sign in H1.

If H1 contains "not equal to" the the test is two tailed.

If H1 contains "<" the the test is left trailed.

If H1 contains ">" the the test is right tailed.

It is important to decide the tail of the test, because it helps in finding p-value and critical value.

If the test one tailed test then p-value is the probability of observing test statistic at only one extreme. While that of two tailed test it is the probability of observing test statistic at both the extremes.

We get only one critical value for one tailed test and two values for two.

That means the tail of the test is crucial part of decision making ( whether to reject or accept H0 ).