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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 theproblem.

When you make a decision to reject or not reject H o , do as follows:

  • If α > 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 α 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.

Practice Key Terms 4

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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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