A systematic way to make a decision of whether to reject or not reject the null hypothesis is to compare the p-value and a preset or preconceived α (also called a "significance level"). A preset α is the probability of a Type I error (rejecting the null hypothesis when the null hypothesis is true). It may or may not be given to you at the beginning of the problem.
When you make a decision to reject or not reject Ho, do as follows:
- If α > p-value, reject Ho. The results of the sample data are significant. There is sufficient evidence to conclude that Ho is an incorrect belief and that the alternative hypothesis, Ha, may be correct.
- If α ≤ p-value, do not reject Ho. The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct.
- When you "do not reject Ho", it does not mean that you should believe that Ho is true. It simply means that the sample data have failed to provide sufficient evidence to cast serious doubt about the truthfulness of Ho.
Conclusion: After you make your decision, write a thoughtful conclusion about the hypotheses in terms of the given problem.