Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 22 of 251 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 0.01 significance level to complete parts (a) through (e) below. 1-propztest prop < 0.08 z = 0.446709780 p = 0.6724576902 p̂ = 0.0876494024 n = 251 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 the claim that less than 8% of treated subjects experienced headaches. c. there is sufficient evidence to warrant rejection of the claim that less than 8% of treated subjects experienced headaches. d. there is not sufficient evidence to support the claim that less than 8% of treated subjects experienced headaches.

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing, if the \(P -\)value \(>\alpha\) (significance level), we fail to reject the null hypothesis. Here, \(\alpha = 0.01\) and from the calculator display \(P=0.6724576902\).
Since \(0.6724576902>0.01\), we fail to reject the null hypothesis.

Step2: Interpret the conclusion

The null hypothesis \(H_0:p = 0.08\) and the alternative hypothesis \(H_1:p<0.08\). Failing to reject the null hypothesis means that there is not enough evidence to support the alternative hypothesis.

Answer:

D. There is not sufficient evidence to support the claim that less than 8% of treated subjects experienced headaches.