In a 2011 study, medical researchers from Rutgers University randomly assigned men to take selenium, vitamin E, both selenium and vitamin E, or placebo. The researchers then followed up to see if the men developed prostate cancer. In this table, the observed count appears above the expected count in each cell.

Reference: Klein, E.A., I.M. Thompson, C.M. Tangen, et al. (21 coauthors). 2011. Vitamin E and the risk of prostate cancer: the selenium and vitamin E cancer prevention trial (SELECT). Journal of the American Medical Association 306: 15491556.
Researchers conducted a chisquare test of homogeneity to determine if there are statistically significant differences among the proportions taking selenium, vitamin E, both selenium and vitamin E, or placebo.
Chisquare test results: chisquare test statistic = 7.7832, Pvalue = 0.051.
The expected counts describe what researchers expect to see if which of the following is correct? Check all that apply.
A) Developing prostate cancer is independent of selenium or vitamin E treatment.
B) The null hypothesis is true.
C) The proportion of subjects with prostate cancer is the same in each treatment group.
D) There is no treatment effect.
Since Pvalue=0.051>0.05 so we fail to reject null hypothesis but Type I error may be committed so Option B. The null hypothesis is true is not correct option. Again Option C is not correct. The correct statement is the proportion of subjects with prostate cancer is insignificantly different. Option D is also not correct. The correct statement is there is insignificant treatment effect. Hence the correct option is:
A) Developing prostate cancer is independent of selenium or vitamin E treatment.
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