Problem
A certain drug is used to treat asthma. In a clinical trial of the drug, 29 of 280 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 $10 \%$ 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. \[ \begin{array}{|l|} \hline \text { 1-PropZTest } \\ \text { prop }<0.1 \\ z=0.199204768 \\ p=0.5789487151 \\ \hat{p}=0.1035714286 \\ n=280 \end{array} \] e. What is the final conclusion? A. There is sufficient evidence to support the claim that less than $10 \%$ of treated subjects experienced headaches. B. There is not sufficient evidence to support the claim that less than $10 \%$ of treated subjects experienced headaches. c. There is sufficient evidence to warrant rejection of the claim that less than $10 \%$ of treated subjects experienced headaches. D. There is not sufficient evidence to warrant rejection of the claim that less than $10 \%$ of treated subjects experienced headaches.
Solution
Step 1 ：Given that the p-value is 0.5789487151 and the significance level is 0.01, we compare these two values.
Step 2 ：Since the p-value is greater than the significance level, we fail to reject the null hypothesis.
Step 3 ：Therefore, there is not sufficient evidence to warrant rejection of the claim that less than 10% of treated subjects experienced headaches.
Step 4 ：\(\boxed{\text{Final Answer: D. There is not sufficient evidence to warrant rejection of the claim that less than 10% of treated subjects experienced headaches.}}\)
