In 2010, a medical research group reported the results of an experiment to evaluate the effectiveness of acupuncture to treat a chronic intestinal condition. A group of volunteers with the chronic intestinal condition agreed to participate in the experiment and be randomly assigned to either a true acupuncture treatment or a placebo treatment. The placebo treatment mimicked the application of acupuncture, but no needle penetrated the skin. Random assignment resulted in 78 subjects receiving acupuncture and 75 subjects receiving the placebo treatment. After receiving 6 treatments over the course of 3 weeks, patients were asked to report whether they had experienced a reduction in the chronic intestinal condition. The table summarizes the data from the study, with expected cell counts in parentheses.
| Yes | No | Total | |
| Acupuncture | 41 (37.2) | 37 (40.8) | 78 |
| Placebo treatment | 32 (35.8) | 43 (39.2) | 75 |
| Total | 73 | 80 | 153 |
Which of the following is true about the chi-square test for homogeneity?
A)The number of subjects randomly assigned to each treatment is not the same; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups.
B)Volunteers do not constitute a random sample from the population of all patients with the chronic intestinal condition; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups.
C)Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met.
D)Not all of the observed cell counts are large enough to satisfy the conditions for applying the chi-square test of homogeneity.
E)Not all of the expected cell counts are large enough to satisfy the conditions for applying the chi-square test for homogeneity.
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