4.5 Carrying Out a Test for a Population Mean or Population Mean Difference

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

• The test statistic for a one-sample t-test for a population mean or population mean difference is x - μt = 0 s n , where t has degrees of freedom n −1. The t-statistic has a t-distribution with degrees of freedom n −1 when the null hypothesis is true.
• The p-value for a one-sample t-test for a population mean or population mean difference is found using the appropriate t-distribution table or technology.

Interpret the p-value of a hypothesis test for a population mean or population mean difference.

• The p-value is the probability of obtaining a test statistic as extreme or more extreme than the test statistic that was observed (i.e., in the direction of the alternative hypothesis) given that the null hypothesis is true. An interpretation of the p-value of a hypothesis test for a population mean or population mean difference should include a statement that the p-value is computed by assuming that the null hypothesis is true (i.e., by assuming that the population mean is equal to the particular value stated in the null hypothesis in context).

Justify a claim about the population based on the results of a hypothesis test for a population mean or population mean difference.

• A formal decision explicitly compares the p-value to the significance level, α. If the p-value ≤α , then reject the null hypothesis, H:00 μμ= . If the p-value > α, then fail to reject the null hypothesis.
• The results of a hypothesis test for a population mean or population mean difference 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 mean or population mean difference is stated in context consistent with, and in terms of, the alternative hypothesis using nondefinitive language. The conclusion should contain a reference to the parameter and the population. 131 Inference for Quantitative Data: Means UNIT 4