Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 18 of 295 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 12% 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 < 0.12 z = - 3.117498701 p = 0.0009119638 p ^ = 0.0610169492 n = 295 a. reject the null hypothesis because the p - value is greater than the significance level, α b. reject the null hypothesis because the p - value is less than or equal to the significance level, α c. fail to reject the null hypothesis because the p - value is less than or equal to the significance level, α d. fail to reject the null hypothesis because the p - value is greater than the significance level, α e. what is the final conclusion? a. there is not sufficient evidence to warrant rejection of the claim that less than 12% of treated subjects experienced headaches b. there is sufficient evidence to warrant rejection of the claim that less than 12% of treated subjects experienced headaches c. there is sufficient evidence to support the claim that less than 12% of treated subjects experienced headaches d. there is not sufficient evidence to support the claim that less than 12% of treated subjects experienced headaches

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing, if the \(P -\)value \(\leq\alpha\) (significance level), we reject the null hypothesis. Here, \(\alpha = 0.01\) and from the calculator display \(p=0.0009119608\). Since \(0.0009119608<0.01\), we reject the null hypothesis.

Step2: Determine the final conclusion

When we reject the null hypothesis in a one - tailed test (claim: \(p < 0.12\)), it means there is sufficient evidence to support the claim.

Answer:

For the first part (rejecting the null hypothesis): B. Reject the null hypothesis because the \(P -\)value is less than or equal to the significance level, \(\alpha\)
For the second part (final conclusion): C. There is sufficient evidence to support the claim that less than \(12\%\) of treated subjects experienced headaches