Significance Testing for AP Statistics
Practice problems for these concepts can be found at:
- Inference for Means and Proportions Multiple Choice Practice Problems for AP Statistics
- Inference for Means and Proportions Free Response Practice Problems for AP Statistics
- Inference for Means and Proportions Review Problems for AP Statistics
- Inference for Means and Proportions Rapid Review for AP Statistics
The steps in the hypothesis-testing procedure is as follows:
- State hypotheses in the context of the problem. The first hypothesis, the null hypothesis, is the hypothesis we are actually testing. The null hypothesis usually states that there is no bias or that there is no distinction between groups. It is symbolized by H0.
The second hypothesis, the alternative hypothesis, is the theory that the researcher wants to confirm by rejecting the null hypothesis. The alternative hypothesis is symbolized by HA. There are three forms for the alternative hypothesis: ≠ , >, or <. That is, if the null is H0: μ1 – μ2 = 0, then HA could be:
- HA: μ1 – μ2 = 0 (this is called a two-sided alternative)
- HA: μ1 – μ2 > 0 (this is a one-sided alternative)
- HA: μ1 – μ2 < 0 (also a one-sided alternative)
(In the case of the one-sided alternative HA: μ1 – μ2 > 0, the null hypothesis is sometimes written H0: μ1 – μ2 ≤ 0.)
If you stated a significance level, the conclusion can be based on a comparison of the P-value with α. If you didn't state a significance level, you can argue your conclusion based on the value of the P-value alone: if it is small, you have evidence against the null; if it is not small, you do not have evidence against the null.
The conclusion can be (1) that we reject H0 (because of a sufficiently small P-value) or (2) that we do not reject H0 (because the P-value is too large). We never accept the null: we either reject it or fail to reject it. If we reject H0, we can say that we accept HA or, preferably, that we have evidence in favor of HA.
Significance testing involves making a decision about whether or not a finding is statistically significant. That is, is the finding sufficiently unlikely so as to provide good evidence for rejecting the null hypothesis in favor of the alternative? The four steps in the hypothesis testing process outlined above are the four steps that are required on the AP exam when doing inference problems. In brief, every test of a hypothesis should have the following four steps:
- State the null and alternative hypotheses in the context of the problem.
- Identify the appropriate test and check that the conditions for its use are present.
- Do the correct mechanics, including calculating the value of the test statistic and the P-value.
- State a correct conclusion in the context of the problem.
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