Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 26 of 292 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. c. what is the p - value? p - value = 0.716 (round to three decimal places as needed.) d. what is the null hypothesis, and what do you conclude about it? identify the null hypothesis. a. ( h_{0}: p<0.08 ) b. ( h_{0}: p>0.08 ) c. ( h_{0}: p = 0.08 ) d. ( h_{0}: p
eq0.08 )

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of no effect or no difference. When testing a claim about a proportion \(p\), if the claim is about a specific value (in this case, the claim is related to \(p = 0.08\) as we are comparing to \(8\%=0.08\)), the null hypothesis is \(H_0:p = 0.08\). The alternative hypothesis \(H_1\) would be \(p<0.08\) (since the claim is that less than \(8\%\) of treated subjects experienced headaches).

Answer:

C. \(H_0:p = 0.08\)