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.
Solution
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.
