Problem
A certain drug is used to treat asthma. In a clinical trial of the drug, 15 of 293 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than $8 \%$ of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below. \[ \begin{array}{l} \text { 1-PropZTest } \\ \text { prop }<0.08 \\ z=-1.817480372 \\ p=0.0345717955 \\ \hat{p}=0.0511945392 \\ n=293 \end{array} \] d. What is the null hypothesis, and what do you conclude about it? Identify the null hypothesis. A. $\mathrm{H}_{0}: \mathrm{p}=0.08$ B. $\mathrm{H}_{0}: \mathrm{p} \neq 0.08$ C. $H_{0}: p>0.08$ D. $H_{0}: p<0.08$
Solution
Step 1 ：The null hypothesis for a proportion test is typically that the proportion equals a certain value. In this case, the null hypothesis is that the proportion of treated subjects who experienced headaches is 8%. Therefore, the null hypothesis is \(H_{0}: p=0.08\).
Step 2 ：Based on the given information, the p-value is 0.0345717955, which is greater than the significance level of 0.01. Therefore, we fail to reject the null hypothesis.
Step 3 ：So, the final answer is \(\boxed{\text{A. } H_{0}: p=0.08}\).
