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 7380153Which 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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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 7380153Which 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.

Isla Preston · Accepted Answer

Introduction:The chi-square test of homogeneity is suggested to be used here, in order to evaluate whether acupuncture is effective in treating a chronic intestinal condition.Explanation:The conditions under which the chi-square test of homogeneity is suitable to use are as follows:1. Random sample: The samples must be collected from the relevant populations using suitable simple random sampling methods in order to ensure that the sample represents the population well, and the results of the hypothesis test can be generalized to the population.2. Independence: The observations must all be independent of each other, and not correlated, across the various categories for a particular population.3. Sample size: The overall sample size should be large enough. As a rule of thumb, an overall sample size of at least 20 is desirable to avoid unnecessarily large probability of Type II error.4. Expected cell count: The expected cell count for each cell must be at least 5 in order for the results of the test to be valid.It is unnecessary to have same sample sizes from the different populations, or observed cell counts greater than 5.The expected cell counts are greater than 5, and the observations are independent of each other.However, the method of data collection is convenience sampling or voluntary response sampling, where the subjects choose themselves to participate in the study. Clearly, no random methods were used to collect the sample.Thus, all the conditions for the test are not met, and the suitable option here is: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.

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