"MigrainesAccording to the Centers for Disease Control, 15.2% of American adults experience migraine headaches. Stress is a major contributor to the frequency and intensity of headaches. A massage therapist feels that she has a technique that can reduce the frequency and intensity of migraine headaches.


a. Determine the null and alternative hypotheses that would be used to test the effectiveness of the massage therapist’s techniques.


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Verified step by step guidance

1. Step 1: Identify the parameter of interest. Here, it is the proportion of American adults who experience migraine headaches, which is given as 15.2%, or 0.152.
2. Step 2: Define the null hypothesis (\(H_0\)). The null hypothesis represents the status quo or no effect. In this case, it states that the massage therapist's technique does not reduce the frequency of migraines, so the proportion remains the same: \(H_0: p = 0.152\).
3. Step 3: Define the alternative hypothesis (\(H_a\)). Since the therapist believes the technique reduces the frequency, the alternative hypothesis should reflect a decrease in the proportion of migraine sufferers: \(H_a: p < 0.152\).
4. Step 4: Understand that these hypotheses set up a one-tailed test because the therapist expects a reduction, not just any change.
5. Step 5: Summarize the hypotheses clearly: \(H_0: p = 0.152\) (no reduction) versus \(H_a: p < 0.152\) (reduction in migraine frequency due to the technique).

Key Concepts

Null and Alternative Hypotheses

In hypothesis testing, the null hypothesis (H0) represents the default or status quo assumption, often stating no effect or no difference. The alternative hypothesis (H1 or Ha) reflects the claim being tested, suggesting a change or effect exists. For this question, H0 would state that the massage technique does not reduce migraine frequency or intensity, while Ha would claim it does.

Hypothesis Testing Framework

Hypothesis testing is a statistical method used to decide whether there is enough evidence to reject the null hypothesis in favor of the alternative. It involves setting up hypotheses, collecting data, calculating a test statistic, and making a decision based on a significance level. This framework helps determine if the massage technique has a statistically significant effect on migraines.

Population Proportion and Its Role in Testing

The problem involves a known population proportion (15.2% of adults with migraines). When testing effectiveness, this baseline proportion is compared to the proportion after applying the massage technique. Understanding how to work with population proportions and sample proportions is essential to formulating hypotheses and interpreting results.