Question

a certain drug is used to treat asthma. in a clinical trial of the drug, 16 of 267 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.
decide whether to reject the null hypothesis. choose the correct answer below.

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing, if \(P - value\leq\alpha\), we reject the null hypothesis \(H_0\). If \(P - value>\alpha\), we fail to reject the null hypothesis \(H_0\). Here, the significance level \(\alpha = 0.01\) and the \(P - value=0.1133079204\) (from the calculator display).

Step2: Compare the P - value and the significance level

We compare \(P - value = 0.1133079204\) and \(\alpha=0.01\). Since \(0.1133079204>0.01\) (i.e., \(P - value>\alpha\)).

Answer:

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