When a result is not extreme enough to reject the null hypothesis

Solution for assignment

Answer this question with 2 different answers.

When a result is not extreme enough to reject the null hypothesis, explain why it is wrong to conclude that your result supports the null hypothesis.

Solution:

There are two approaches for answering this question. First approach is the critical value approach and second is p-value approach. Because we use these two values for rejecting or do not rejecting the null hypothesis. That is, decision is based on these two values. We compare critical value with the test statistic value and then take decision regarding the null hypothesis. Also, we compare p-value with the level of significance alpha value and then we decide whether reject or do not reject the null hypothesis. Let us see the two answers for above questions in detail.

The result is not extreme enough to reject the null hypothesis, when test statistical value is less than the critical value. For any type of hypothesis test, we first establish the null and alternative hypothesis. In so many conditions, our alternative hypothesis is nothing but the claim which we have to test by using the available data. For this test we find the test statistic value. We find the critical value according to given confidence level. Then we use the decision rule for rejecting or do not rejecting the null hypothesis. This decision rule is given as below:

Reject the null hypothesis if the test statistic value is greater than critical value. Do not reject the null hypothesis if the critical value is greater than the test statistic value.

The result is not extreme enough to reject the null hypothesis, when the p-value is greater than the level of significance alpha value. We either use the critical value approach or p-value approach for taking decision regarding null hypothesis. The decision rule for p-value approach is given as below:

Reject the null hypothesis if the p-value is less than level of significance alpha value. We do not reject the null hypothesis if the p-value is greater than the level of significance alpha value. Remember that p-value is nothing but the probability of rejection area under the curve.

Hope that this solution will help you in understanding the concept of decision rule for null hypothesis. Thank you. Have a great day ahead. ☺