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 thespeech the same n people are asked the same question.The responses can be entered in a table as follows:S FS x1 x2F x3 x4AfterBeforewhere x1 1 x2 1 x3 1 x4 5 n. Let p1, p2, p3, and p4denote the four cell probabilities, so that p1 5 P(S beforeand S after), and so on. We wish to test the hypothesis thatthe true proportion of supporters (S) after the speech hasnot increased 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 differencein success probabilities.c. When n is large, it can be shown that the rv (Xi 2 Xj)ynhas approximately a normal distribution with variancegiven by [pi 1 pj 2 (pi 2 pj)2]yn. Use this to constructa test statistic with approximately a standard normaldistribution when H0 is true (the result is calledMcNemars test).d. If x1 5 350, x2 5 150, x3 5 200, and x4 5 300,what do you conclude?

STAT 2004 WEEK 9 BERNOULLI DISTRIBUTION In a Bernoulli distribution, an outcome has two possibilities: success or failure. o Success- What we were interested in happened. o Success is represented by a 1, while failure is represented by a 0. Probability of success is represented by a p. For a Bernoulli random...