Just before a mayoral election a local newspaper polls 450 voters in an attempt

Question

Just before a mayoral election a local newspaper polls 450 voters in an attempt to predict the winner. Suppose that the candidate Johnny Comlately has 53% of the votes among all voters in a two-way race. What is the probability that the newspaper's sample will predict Johnny Comlately losing the election? 0.1248 0.1003 0.0865 0.0695 In repeated polling of n = 450 voters, 95% of sample proportions would deviate from pi = 0.53, in either direction, by no more than _____ (or _____ percentage points). 0.034 0.039 0.046 0.052 In order to make the probability of wrongly predicting loss at most 5%, the minimum number of voters to be included in the sample should be n = _____? 625 698 745 940

Explanation / Answer

23) here std error=(p(1-p)/n)1/2=0.0235

hence P(X<0.5)=P(Z<(0.5-0.53)/0.0235)=P(Z<-1.275)=0.1003; option b

24) for 95% , z=1.96

std error =(p(1-p)/n)1/2=0.0253

hence margin of error =z*std error =0.046 ; option c

25)z=1.6448

margin of error E =0.03

hence sample size =(p(1-p)(z/E)2~745

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