The Hypothesis-Testing Procedure for AP Statistics (page 2)

Practice problems for these concepts can be found at:

• Confidence Intervals and Introduction to Inference Multiple Choice Practice Problems for AP Statistics
• Confidence Intervals and Introduction to Inference Free Response Practice Problems for AP Statistics
• Confidence Intervals and Introduction to Inference Review Problems for AP Statistics
• Confidence Intervals and Introduction to Inference Rapid Review for AP Statistics

So far we have used confidence intervals to estimate the value of a population parameter (μ, p, μ₁ – μ₂, p₁ – p₂). In this lesson, we test whether the parameter has a particular value or not. We might ask if p₁ – p₂ = 0 or if μ = 3, for example. That is, we will test the hypothesis that, say, p₁ – p₂ = 0. In the hypothesis-testing procedure, a researcher does not look for evidence to support this hypothesis, but instead looks for evidence against the hypothesis. The process looks like this.

• State the null and alternative 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. An example of a typical null hypothesis would be H₀: μ₁ – μ₂ = 0 or H₀: μ₁ = μ₂. This is the hypothesis that μ₁ and μ₂ are the same, or that populations 1 and 2 have the same mean. Note that μ₁ and μ₂ must be identified in context (for example, μ₁ = the true mean score before training).

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 H_A or H_a. There are three possible forms for the alternative hypothesis: ≠, >, or <. If the null is H₀: μ₁ – μ₂ = 0, then H_A could be:

H_A: μ₁ – μ₂ ≠ 0 (this is called a two-sided alternative

or

H_A: μ₁ – μ₂ > 0 (this is a one-sided alternative)

or

H_A: μ₁ – μ₂ < 0 (also a one-sided alternative).

(In the case of the one-sided alternative H_A: μ₁ – μ₂ > 0, the null hypothesis is sometimes written: H₀: μ₁ – μ₂ ≤ 0. This actually makes pretty good sense: if the researcher is wrong in a belief that the difference is greater than 0, then any finding less than or equal to 0 fails to provide evidence in favor of the alternative.)

• Identify which test statistic (so far, that's z or t) you intend to use and show that the conditions for its use are present. We identified the conditions for constructing a confidence interval in the first two sections of this chapter. We will identify the conditions needed to do hypothesis testing in the following chapters. For the most part, they are similar to those you have already studied.

If you are going to state a significance level α it can be done here.

• Compute the value of the test statistic and the P-value.
• Using the value of the test statistic and/or the P-value, give a conclusion in the context of the problem