Decision and Conclusion

Learning Outcomes

  • Explain what a p-value means about a given test statistic

Decision and Conclusion

A systematic way to make a decision of whether to reject or to 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 to not reject H0, do as follows:

  • If α > p-value, reject H0. The results of the sample data are significant. There is sufficient evidence to conclude that H0 is an incorrect belief and that the alternative hypothesis, Ha, may be correct.
  • If α ≤ p-value, do not reject H0. 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 H0,” it does not mean that you should believe that H0 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.

Example 2

When using the p-value to evaluate a hypothesis test, it is sometimes useful to use the following memory device:

If the p-value is low, the null must go.

If the p-value is high, the null must fly.

This memory aid relates a p-value less than the established alpha (the p is low) as rejecting the null hypothesis and, likewise, relates a p-value higher than the established alpha (the p is high) as not rejecting the null hypothesis.

Fill in the blanks.

Reject the null hypothesis when ______________________________________.

The results of the sample data _____________________________________.

Do not reject the null when hypothesis when __________________________________________.

The results of the sample data ____________________________________________.

try it 2

It’s a Boy Genetics Labs claim their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows: H0: p = 0.50, Ha: p > 0.50

α = 0.0

p-value = 0.025

Interpret the results and state a conclusion in simple, non-technical terms.