Noroviruses Cause Roughly 21 Million Cases of Gastroenteritis ("Stomach Flu")

Noroviruses cause roughly 21 million cases of gastroenteritis ("stomach flu") annually in the United States. A study examined the effectiveness of a new norovirus vaccine. Healthy adult volunteers received, at random, either the vaccine or a placebo. They were then exposed to the norovirus. In all, 14 of the 38 vaccinated subjects suffered from gastroenteritis compared with 27 of the 39 subjects who received a placebo. We want to know if this study provides evidence that an outcome of gastroenteritis depends on the treatment received. What can we state about the chi-square test in this situation?

A) The test is not valid because the sample sizes are small.
B) The test is not valid because some observed counts are too small.
C) The test is valid because the t expected counts are large enough and the treatments were given randomly.
D) The test is valid because the study is a randomized experiment.