Question

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 28 of 257 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 11​% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts​ (a) through​ (e) below.

Answer 1

The question involves applying hypothesis testing using the normal approximation to the binomial distribution to determine if a drug leads to headaches in less than 11% of treated subjects.

Step-by-step explanation:

The question asks us to perform a hypothesis test to determine if a certain drug causes headaches in fewer than 11% of treated subjects, based on clinical trial data provided.

First, we need to define the null hypothesis (H0) as the proportion of treated subjects experiencing headaches being 11% or more. The alternative hypothesis (H1) is that less than 11% of treated subjects experience headaches.

Using the normal approximation to the binomial distribution and the data given (28 out of 257 subjects experienced headaches), we would calculate the test statistic and the p-value and compare it to the significance level of 0.05. If the p-value is less than 0.05, we reject the null hypothesis, suggesting that the drug does cause headaches in fewer than 11% of treated subjects.