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Hypothesis Testing of Single Mean and Single Proportion: Decision and Conclusion

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

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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 αα (also called a "significance level"). A preset αα 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 HoHo, do as follows:

  • If α>p-valueα>p-value, reject HoHo. The results of the sample data are significant. There is sufficient evidence to conclude that HoHo is an incorrect belief and that the alternative hypothesis, HaHa, may be correct.
  • If α≤p-valueα≤p-value, do not reject HoHo. The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis, HaHa, may be correct.
  • When you "do not reject HoHo", it does not mean that you should believe that HoHo is true. It simply means that the sample data has failed to provide sufficient evidence to cast serious doubt about the truthfulness of HoHo.

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

Glossary

Hypothesis:
A statement about the value of a population parameter. In case of two hypotheses, the statement assumed to be true is called the null hypothesis (notation H0H0 size 12{H rSub { size 8{0} } } {}) and the contradictory statement is called the alternate hypothesis (notation HaHa size 12{H rSub { size 8{a} } } {}).
Level of Significance of the Test :
Probability of a Type I error (reject the null hypothesis when it is true). Notation: αα. In hypothesis testing, the Level of Significance is called the preconceived αα or the preset αα.
p-value:
The probability that the event will happen purely by chance assuming the null hypothesis is true. The smaller the p-value, the stronger the evidence is against the null hypothesis.
Type 1 Error:
The decision is to reject the Null hypothesis when, in fact, the Null hypothesis is true.

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