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 p ^ = 0.0876494624 n = 251 b. h 0 : p > 0.08 c. h 0 : p = 0.08 d. h 0 : p < 0.08 decide whether to reject the null hypothesis. choose the correct answer below. a. fail to 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 greater than 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. reject the null hypothesis because the p - value is less than or equal to the significance level, α.

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 \(H_0\). If the \(P -\)value \(\leq\alpha\), we reject the null hypothesis \(H_0\). Here, \(\alpha = 0.01\) and from the calculator display \(p=0.6724576902\) (the \(P -\)value).

Step2: Compare the \(P -\)value and \(\alpha\)

Since \(0.6724576902>0.01\) (i.e., \(P -\)value \(>\alpha\)).

Answer:

A. Fail to reject the null hypothesis because the \(P -\)value is greater than the significance level, \(\alpha\).