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Consider an unbalanced study with six subjects, identified as A, B, C, D, E and G. In the actual study, • Subjects A and B are assigned to the first treatment, and the other subjects are assigned to the second treatment. • There are exactly two successes, obtained by A and C. This information is needed for parts (a)–(c) below. (a) Compute the observed value of the test statistic. (b) Assume that the Skeptic is correct. Determine the observed value of the test statistic for the assignment that places D and E on the first treatment, and the remaining subjects on the second treatment. (c) We have obtained the sampling distribution of the test statistic on the assumption that the Skeptic is correct. It also is possible to obtain a sampling distribution of the test statistic if the Skeptic is wrong provided we specify exactly how the Skeptic is in error. These new sampling distributions are used in the study of statistical power which is briefly described in Chapter 7 of the text. Assume that the Skeptic is correct about subjects A and G, but incorrect about subjects B, C, D and E. For the assignment that puts D and G on the first treatment, and the other subjects on the second treatment, determine the response for each of the six subjects.
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