\( \left\lvert\, \leftarrow \quad \begin{array}{l}\text { Consider a drug that is used to help prevent blood clots in certain patients. In clinical trials, among } 5754 \text { patients treated with this drug, } \\ 157 \text { developed the adverse reaction of nausea. Use a } 0.10 \text { significance level to test the claim that } 3 \% \text { of users develop nausea. Does } \\ \text { nausea appear to be a problematic adverse reaction? } \\ \text { Identify the null and alternative hypotheses for this test. Choose the correct answer below. } \\ \text { A. } H_{0}: p=0.03 \\ H_{1}: p \neq 0.03 \\ \text { B. } H_{0}: p=0.03 \\ H_{1}: p<0.03 \\ \text { C. } H_{0}: p \neq 0.03 \\ H_{1}: p=0.03 \\ \text { D. } H_{0}: p=0.03 \\ H_{1}: p>0.03\end{array}\right. \)

To solve this problem, we need to identify the null and alternative hypotheses based on the information provided. 1. **Understanding the Problem:** - We are testing the claim that 3% of users develop nausea. - The null hypothesis (\(H_0\)) typically represents the status quo or a statement of no effect, while the alternative hypothesis (\(H_1\)) represents what we are trying to find evidence for. 2. **Setting Up the Hypotheses:** - The null hypothesis (\(H_0\)) states that the proportion of patients who develop nausea is equal to 3%, which can be expressed as: \[ H_0: p = 0.03 \] - The alternative hypothesis (\(H_1\)) is what we are testing against. Since we want to determine if nausea is a problematic adverse reaction, we are interested in whether the proportion is different from 3%. This leads us to: \[ H_1: p \neq 0.03 \] 3. **Choosing the Correct Answer:** - Based on the hypotheses we have established, the correct choice is: - **A.** \(H_0: p = 0.03\) and \(H_1: p \neq 0.03\) Thus, the null and alternative hypotheses for this test are: - \(H_0: p = 0.03\) - \(H_1: p \neq 0.03\)