A certain drug is used to treat asthma. In a clinical trial of the drug, 30 of 277 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 0.05 significance level to complete parts (a) through (e) below.
\[
\begin{array}{|l|}
\hline \text {-PropzTest } \\
\text { prop }< 0.08 \\
z=1.736349998 \\
p=0.9587490161 \\
\hat{p}=0.1083032491 \\
n=277
\end{array}
\]
B. $\mathrm{H}_{0}: \mathrm{p} \neq 0.08$
C. $\mathrm{H}_{0}: \mathrm{p}=0.08$
D. $\mathrm{H}_{0}: \mathrm{p}< 0.08$
Decide whether to reject the null hypothesis. Choose the correct answer below.
A. Reject the null hypothesis because the P-value is greater than the significance level, $\alpha$.
B. Fail to reject the null hypothesis because the P-value is greater than the significance level, $\alpha$.
C. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$.
D. Reject the null hypothesis because the P-value is less than or equal to the significance level, $\alpha$.
e. What is the final conclusion?
A. There is sufficient evidence to support the claim that less than $8 \%$ of treated subjects experienced headaches.
B. There is not sufficient evidence to warrant rejection of thic claim that less than $8 \%$ of treated subjects experienced headaches.
C. There is not sufficient evidence to support the claim that less than $8 \%$ of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than $8 \%$ of treated subjects experienced headaches.
Answer
The null hypothesis for this test is that the proportion of subjects who experienced headaches is equal to 8%, or p = 0.08. This is represented by option C. $\mathrm{H}_{0}: \mathrm{p}=0.08$. Given the p-value of 0.9587490161, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. This is because the p-value is not less than or equal to the significance level, α. Therefore, the correct answer is B. Fail to reject the null hypothesis because the P-value is greater than the significance level, α. Finally, since we failed to reject the null hypothesis, there is not sufficient evidence to support the claim that less than 8% of treated subjects experienced headaches. This is represented by option C. There is not sufficient evidence to support the claim that less than $8 \%$ of treated subjects experienced headaches.
Step 1 ：The null hypothesis for this test is that the proportion of subjects who experienced headaches is equal to 8%, or p = 0.08. This is represented by option C. $\mathrm{H}_{0}: \mathrm{p}=0.08$. Given the p-value of 0.9587490161, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. This is because the p-value is not less than or equal to the significance level, α. Therefore, the correct answer is B. Fail to reject the null hypothesis because the P-value is greater than the significance level, α. Finally, since we failed to reject the null hypothesis, there is not sufficient evidence to support the claim that less than 8% of treated subjects experienced headaches. This is represented by option C. There is not sufficient evidence to support the claim that less than $8 \%$ of treated subjects experienced headaches.
