Sometimes experiments involving success or failureresponses are run in a paired or

Chapter 9, Problem 56

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Sometimes experiments involving success or failureresponses are run in a paired or before/after manner.Suppose that before a major policy speech by a politicalcandidate, n individuals are selected and asked whether (S)or not (F) they favor the candidate. Then after the speech thesame n people are asked the same question. The responsescan be entered in a table as follows:[(m 2 x)/(mx) 1 (n 2 y)/(ny)]1/2ln(u) u 5 p 1/p 2p1 2 p2u 5 p1/p2where . Let , and p4 denotethe four cell probabilities, so that (S before and Safter), and so on. We wish to test the hypothesis that the trueproportion of supporters (S) after the speech has notincreased against the alternative that it has increased.a. State the two hypotheses of interest in terms of p1, p2, p3,and p4.b. Construct an estimator for the after/ before difference insuccess probabilities.c. When n is large, it can be shown that the rv hasapproximately a normal distribution with variance givenby . Use this to construct a teststatistic with approximately a standard normal distributionwhen H0 is true (the result is called McNemars test).d.If , and ,what do you conclude?