Questions 23-25 are based on the following information Just before a mayoral ele

Question

Questions 23-25 are based on the following information 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.   23 What is the probability that the newspaper’s sample will predict Johnny Comlately losing the election? a 0.1248 b 0.1003 c 0.0865 d 0.0695 24 In repeated polling of n = 450 voters, 95% of sample proportions would deviate from = 0.53, in either direction, by no more than ______ (or _____ percentage points). a 0.034 b 0.039 c 0.046 d 0.052 25 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 = ______? a 625 b 698 c 745 d 940 Questions 23-25 are based on the following information 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.   23 What is the probability that the newspaper’s sample will predict Johnny Comlately losing the election? a 0.1248 b 0.1003 c 0.0865 d 0.0695 24 In repeated polling of n = 450 voters, 95% of sample proportions would deviate from = 0.53, in either direction, by no more than ______ (or _____ percentage points). a 0.034 b 0.039 c 0.046 d 0.052 25 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 = ______? a 625 b 698 c 745 d 940

Explanation / Answer

23) here p=0.53

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

therefore probability of losing =P(P<0.5)=P(Z<(0.5-0.53)/0.0235)=P(Z<-1.2751)=0.1003

24)for 95% CI, z=1.96

hence margin of errror =z*std error =0.046

25)for 90% CI, z=1.64

here margin of error =E=0.03

and p=0.53

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

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