5.3 Hypothesis testing of single mean and single proportion: decision

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 $\alpha$ (also called a "significance level") . A preset $\alpha$ 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 theproblem.

When you make a decision to reject or not reject $H_o$ , do as follows:

• If $\alpha >\text{p-value}$ , reject $H_o$ . The results of the sample data are significant. There is sufficient evidence to conclude that $H_o$ is an incorrect belief and that the alternative hypothesis , $H_a$ , may be correct.
• If $\alpha \le \text{p-value}$ , do not reject $H_o$ . The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis, $H_a$ , may be correct.
• When you "do not reject $H_o$ ", it does not mean that you should believe that $H_o$ is true. It simply means that the sample data have failed to provide sufficient evidence to cast serious doubt about the truthfulness of $H_o$ .

Conclusion: After you make your decision, write a thoughtful conclusion about the hypotheses in terms of the given problem.