3.7 Carrying Out a Test for a Population Proportion

Calculate an appropriate test statistic and p-value for testing a hypothesis about a population proportion.

• The test statistic for testing a population proportion is pp n  0 00 1 . The z-statistic has a standard normal distribution when the null hypothesis is true.
• The distribution of the test statistic assuming the null hypothesis is true (null distribution) can be approximated by a probability model (e.g., a theoretical distribution such as the standard normal distribution).
• The p-value of a one-sample z-test for a population proportion is found from the standard normal distribution using a table or technology.

Justify a claim about the population based on the results of a hypothesis test for a population proportion.

• The significance level of a hypothesis test, denoted by α, is the predetermined probability of rejecting the null hypothesis given that it is true. The significance level may be given or determined by the researcher. The relationship between a p-value and the significance level of a hypothesis test determines whether a result is statistically significant.
• A formal decision in a hypothesis test explicitly compares the p-value to the significance level, α. If the p-value , then reject the null hypothesis, 0 pp .0 If the p-value , then fail to reject the null hypothesis.
• Rejecting the null hypothesis means there is convincing statistical evidence to support the alternative hypothesis. Failing to reject the null hypothesis means there is not convincing statistical evidence to support the alternative hypothesis.
• A hypothesis test can lead to rejecting or not rejecting the null hypothesis but can never lead to concluding or proving that the null hypothesis is true. Lack of statistical evidence for the alternative hypothesis is not the same as evidence for the null hypothesis.
• The results of a hypothesis test for a population proportion can serve as the statistical reasoning to support the answer to an investigative question about the population that was sampled.
• A conclusion for the hypothesis test for a population proportion is stated in context consistent with, and in terms of, the alternative hypothesis using non-definitive language. The conclusion should contain a reference to the parameter and the population. Inference for Categorical Data: Proportions UNIT 3 98