1. **State the problem:** We want to test if there is a difference in the population mean cholesterol levels between people with the medication ($\mu_1$) and people with the placebo ($\mu_2$). 2. **Define hypotheses:** - Null hypothesis ($H_0$): $\mu_1 = \mu_2$ (means are equal, no effect of medication) - Alternative hypothesis ($H_1$): $\mu_1 \neq \mu_2$ (means are different, medication has an effect) 3. **Identify the type of test:** Since the alternative hypothesis is $\mu_1 \neq \mu_2$, this is a **two-tailed test**. 4. **Summary:** $$ H_0: \mu_1 = \mu_2 $$ $$ H_1: \mu_1 \neq \mu_2 $$ This means we are testing for any difference, whether $\mu_1$ is greater or less than $\mu_2$. 5. **Explanation:** A two-tailed test checks for differences in both directions, unlike left-tailed (checks if $\mu_1 < \mu_2$) or right-tailed (checks if $\mu_1 > \mu_2$). This completes the first step of hypothesis testing for the given problem.