Just before a mayoral election a local newspaper polls 400 voters in an attempt

Question

Just before a mayoral election a local newspaper polls 400 voters in an attempt to predict the winner. Suppose that the candidate Johnny Comlately has 47% of the votes in a two-way race. What is the probability that the newspaper's sample will predict Johnny Comlately winning the election? 0.1151 0.1362 0.1539 0.1665 In repeated polling of n = 400 voters, 95% of sample proportions would deviate from n = 0.47, in either direction, by no more than ______ (or ______ percentage points). 0.055 0.049 0.042 0.034 In order to make the probability of wrongly predicting victory at most 5%, the minimum number of voters to be included in the sample should be n =______? 698 745 842 940

Explanation / Answer

38) std error =(p(!-p)/n)1/2 =0.025

hence P(P>0.5)=1-P(P<0.5)=1-P(Z<(0.5-0.47)/0.025)=1-P(Z<1.2022)=1-0.8849=0.1151

option A

39)for 95% CI, z=1.96

margin of error =z*std error =1.96*0.025=0.049

option b

40)n=p(1-p)*(z/E)2 =745

option B

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