Question

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 27 of 261 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 ​% 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. a. Is the test​ two-tailed, left-tailed, or​ right-tailed? ​Left-tailed test Right tailed test ​Two-tailed test

Answer 1

A hypothesis test is conducted to determine if less than a certain percentage of subjects treated with a drug experience headaches. The alternative hypothesis suggests a decrease, thus a left-tailed test is appropriate for this situation.

Step-by-step explanation:

The question revolves around determining whether a specific drug treatment results in fewer headache incidents among treated subjects than a given percentage threshold, which requires a hypothesis test to answer.

If the claim is that less than a certain percentage of treated subjects experienced headaches, then the alternative hypothesis (Ha) would suggest the proportion is lower than the specified value. This would lead us to perform a left-tailed test because we are looking for evidence to support a decrease in the proportion (indicating a one-directional alternative).

Therefore, based on the information given, where the manufacturer's data indicated that 27 of the 261 treated subjects experienced headaches, one would conduct a left-tailed test. A left-tailed test is appropriate when the alternative hypothesis suggests that the parameter of interest is less than a particular value.

Since the clinical trial aims to prove the drug causes fewer headaches (which means less than a certain threshold), it aligns with the reasoning for a left-tailed hypothesis test.