Question

a certain drug is used to beat 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. d. what is the null hypothesis, and what do you conclude about it? identify the null hypothesis. a. ( h_{0}: p
eq 0.12 ) b. ( h_{0}: p = 0.12 ) c. ( h_{0}: p > 0.12 ) d. ( h_{0}: p < 0.12 ) decide whether to reject the null hypothesis. choose the correct answer below. a. reject the null hypothesis because the p - value is greater than the significance level, ( alpha ). b. reject the null hypothesis because the p - value is less than or equal to the significance level, ( alpha ). c. fail to reject the null hypothesis because the p - value is less than or equal to the significance level, ( alpha ). d. fail to reject the null hypothesis because the p - value is greater than the significance level, ( alpha ).

Explanation:

Step1: Identify the null hypothesis

The null hypothesis \(H_0\) is a statement of equality. In hypothesis testing for a proportion \(p\), when the claim is about a specific proportion (here the claim is related to \(p = 0.12\) as the reference value for comparison), the null hypothesis is \(H_0:p = 0.12\).

Step2: Use the P - value rule

The significance level \(\alpha=0.01\). The P - value from the calculator display is \(P = 0.0009113616\).
The rule for hypothesis testing is: If \(P\leq\alpha\), we reject \(H_0\); if \(P > \alpha\), we fail to reject \(H_0\).
Since \(0.0009113616<0.01\) (i.e., \(P\leq\alpha\))

Answer:

For the null hypothesis: B. \(H_0:p = 0.12\)
For the decision: B. Reject the null hypothesis because the P - value is less than or equal to the significance level, \(\alpha\)