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.
Answer
\(\boxed{\text{Final Answer: D. There is not sufficient evidence to warrant rejection of the claim that less than 10% of treated subjects experienced headaches.}}\)
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 ：\(\boxed{\text{Final Answer: D. There is not sufficient evidence to warrant rejection of the claim that less than 10% of treated subjects experienced headaches.}}\)
