certain drug is used to treat asthma. In a clinical trial of the drug, 29 of 261 treated subjects experienced headaches (based on ata from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than $9 \%$ of treated ubjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 ignificance level to complete parts (a) through (e) below.
\[
\begin{array}{l}
\text { 1-PropZTest } \\
\text { prop }< 0.09 \\
z=1.191761618 \\
p=0.8833226352 \\
\hat{p}=0.1111111111 \\
n=261
\end{array}
\]
C. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$.
Reject the null hypothesis because the P-value is greater than the significance level, $\alpha$.
e. What is the final conclusion?
A. There is not sufficient evidence to support the claim that less than $9 \%$ of treated subjects experienced headaches.
B. There is not sufficient evidence to warrant rejection of the claim that less than $9 \%$ of treated subjects experienced headaches.
C. There is sufficient evidence to support the claim that less than $9 \%$ of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than $9 \%$ of treated subjects experienced headaches.
Answer
\(\boxed{\text{The final conclusion is B. There is not sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches.}}\)
Step 1 ：The null hypothesis in this case is that less than 9% of treated subjects experienced headaches.
Step 2 ：The P-value given is 0.8833226352 and the significance level is 0.05.
Step 3 ：If the P-value is less than or equal to the significance level, we reject the null hypothesis. If the P-value is greater than the significance level, we fail to reject the null hypothesis.
Step 4 ：In this case, the P-value is greater than the significance level, so we fail to reject the null hypothesis.
Step 5 ：This means that there is not enough evidence to support the claim that less than 9% of treated subjects experienced headaches.
Step 6 ：\(\alpha = 0.05\)
Step 7 ：\(p_{\text{value}} = 0.8833226352\)
Step 8 ：The output will be 'Fail to reject the null hypothesis' because the P-value is greater than the significance level.
Step 9 ：This means that there is not enough evidence to reject the claim that less than 9% of treated subjects experienced headaches.
Step 10 ：\(\boxed{\text{The final conclusion is B. There is not sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches.}}\)
