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Hypothesis Testing for Proportions Study Guide (page 4)

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Updated on Oct 5, 2011

Step 4: Decide Whether or Not to Reject the Null Hypothesis

If the null hypothesis were true, then we would expect to see a test statistic this extreme or more extreme about 15% of the time. This is not very unusual. Flipping a coin three times and obtaining all heads occurs less frequently (12.5%). If we use any traditional significance level, such as α = 0.05 or 0.01, then the p-value would be greater than the significance level. For all of these reasons, we would not reject the null hypothesis.

Step 5: State Conclusions in the Context of the Study

There is not sufficient evidence to conclude that more than half of the students at this large university regularly take afternoon or evening naps. It is important to note that = 0.567 is greater than 50%, so the sample is consistent with the null hypothesis. However, there is a possibility that p = 0.50 and sampling variability caused to be this large. If = 0.567 is enough larger than 0.50 to be practically important, the researcher may choose to conduct another study using a larger sample size.

Hypothesis Testing For Proportions In Short

Statistical hypothesis testing is a fundamental tool in research today. The investigator takes the research hypothesis as the alternative hypothesis if at all possible. Two types of errors are possible. If a true null hypothesis is rejected, a type I error has been committed. If we do not reject a false null hypothesis, a type II error has been committed. The probability of a type I error is controlled. There are five steps to conducting a statistical hypothesis test. It is important to carefully complete each step.

Find practice problems and solutions for these concepts at Hypothesis Testing for Proportions Practice Exercises.

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