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Let's address each part of this question one by one:

### Part (a) - Identify the population(s)
The population in this context is **all individuals who take the allergy medication**. The drug company and the researcher are both making claims about the effect of this medication on this specific group of people.

### Part (b) - What is the variable being examined for individuals in the population?
The variable being examined here is **whether an individual who takes the allergy medication experiences headaches**. This is a categorical variable with two possible outcomes: "yes" (the individual experiences headaches) or "no" (the individual does not experience headaches).

### Part (c) - Write the null and alternative hypothesis
In hypothesis testing, the null and alternative hypotheses for this scenario would be:

- **Null Hypothesis (\( H_0 \))**: The proportion of individuals who experience headaches after taking the medication is \( p = 0.05 \), or 5%.
- **Alternative Hypothesis (\( H_a \))**: The proportion of individuals who experience headaches after taking the medication is \( p > 0.05 \), or more than 5%.

The alternative hypothesis reflects the medical researcher’s belief that the true percentage of individuals experiencing headaches is higher than the company's claimed 5%.

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### Related Questions:
1. What statistical test would be appropriate to evaluate this hypothesis?
2. How would sample size affect the reliability of the hypothesis test in this context?
3. What might be some potential sources of bias in studying this medication’s side effects?
4. How could confidence intervals be used in conjunction with this hypothesis test?
5. What other variables could be examined to study the side effects of this medication comprehensively?

### Tip:
When forming hypotheses, make sure the null hypothesis represents the status quo or the original claim, while the alternative reflects the research question or belief you wish to investigate.

A drug company claims that an allergy medication causes headaches in 5% of those who take it. A medical researcher believes that more than 5% of those who take the drug actually get headaches.

 a. Identify the population(s)
 b. What is the variable being examined for individuals in the population?
 c. Write the null and alternative hypothesis.

Explore hypothesis testing in this problem where a drug company's claim about headache incidence from an allergy medication is questioned by a researcher. Learn how to define populations, variables, and set up null and alternative hypotheses for proportions.

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