Problem
A certain drug is used to treat asthma. In a clinical trial of the drug, 30 of 286 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 $9 \%$ 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. \[ \begin{array}{|l|} \hline \text { 1-Prop2Test } \\ \text { prop }<0.09 \\ z=0.880206622 \\ p=0.8106263066 \\ \hat{p}=0.1048951049 \\ n=286 \end{array} \] (Round to two decimal places as needed.) c. What is the P-value? $P$-value $=0.8106$ (Round to four decimal places as needed.) d. What is the null hypothesis, and what do you conclude about it? Identify the null hypothesis. A. $\mathrm{H}_{0}: \mathrm{p}>0.09$ B. $\mathrm{H}_{0}: \mathrm{p}=0.09$ c. $H_{0}: p \neq 0.09$ D. $\mathrm{H}_{0}: \mathrm{p}<0.09$ Clear all Check answer
Solution
Step 1 ：The null hypothesis for this test is B. $H_{0}: p=0.09$. This is because the null hypothesis is always a statement of no effect or no difference. In this case, it is the claim that the proportion of treated subjects who experienced headaches is 9%. Given the P-value of 0.8106, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that less than 9% of treated subjects experienced headaches.
