Question

a medical study was investigating if getting a flu shot actually reduced the risk of developing the flu. from a group of adult volunteers, researchers randomly assigned half to receive an injection that contained the drug believed to reduce the risk of getting the flu and the other half to receive an injection containing no active ingredient (i.e sugar water). a hypothesis test was performed and a p - value of 0.0002 was obtained. which of the following statements is true?
choose the correct answer below.
a. the small p - value indicates that there is not enough evidence to reject the null hypothesis. therefore, it cannot be concluded that the reduction in the risk of getting the flu was caused by the flu shot.
b. the small p - value indicates strong evidence to reject the null hypothesis. even though an experiment was performed, causation cannot be inferred. that is, it cannot be concluded that the reduction in the risk of getting the flu was caused by the flu shot.
c. the small p - value indicates strong evidence to reject the null hypothesis. because an experiment was not performed, it cannot be concluded that the reduction in the risk was caused by the flu shot.
d. the small p - value indicates strong evidence to reject the null hypothesis. because an experiment was performed, it can be concluded that the reduction in the risk of getting the flu was caused by the flu shot

Explanation:

• A small p - value (in this case \(p = 0.0002\)) is evidence against the null hypothesis. If \(p\) - value \(<\alpha\) (commonly \(\alpha=0.05\) or \(\alpha = 0.01\)), we reject the null hypothesis. Here, since \(0.0002<0.05\) and \(0.0002 < 0.01\), we have strong evidence to reject the null hypothesis.
• The study is an experiment (volunteers were randomly assigned to treatment and control groups). In an experiment, when we reject the null hypothesis, we can infer causation.

Answer:

D. The small p - value indicates strong evidence to reject the null hypothesis. Because an experiment was performed, it can be concluded that the reduction in the risk of getting the flu was caused by the flu shot.