In a certain election, 57% of the women voters voted for Candidate A, while only
ID: 3256085 • Letter: I
Question
In a certain election, 57% of the women voters voted for Candidate A, while only 52% of men voters voted for Candidate A. An exit poll of 163 women and 212 men was conducted. Let [^(p)]1 and [^(p)]2 denote sample proportions of women and men voters respectively who voted for Candidate A.
Answer all the questions below (where appropriate) as a fraction not as a percentage.
What is the expected value of [^(p)]1? [Answer to two decimal places.]
What is the standard deviation of [^(p)]1? [Answer to four decimal places.]
What is the expected value of [^(p)]2? [Answer to two decimal places.]
What is the standard deviation of [^(p)]2? [Answer to four decimal places.]
What is the expected value of [^(p)]1 [^(p)]2? [Answer to two decimal places.]
What is the standard deviation of [^(p)]1 [^(p)]2? [Answer to four decimal places.]
What is the probability that the difference [^(p)]1 [^(p)]2 will be larger than 0.0900000000000001? [Answer to four decimal places.]
Explanation / Answer
What is the expected value of p1=
0.57
What is the standard deviation of p1=
p1*(1-p1) = .57*(1-.57)=.245
What is the expected value of p1=
0.52
What is the standard deviation of p2=
p2*(1-p2) = .52*(1-.52)=.2496
What is the expected value of p1-p2 =
0.57-0.52 = 0.05
What is the standard deviation of p1-p2
pooled standard deviation p=(n1p1*n2*p2)/(n1+n2) =
=(0.57*163+0.52*212)/(163+212)
=0.54
What is the probability that the difference [^(p)]1 [^(p)]2 will be larger than 0.09
we need to compute stand ard error SE=sqrt[p(1-p)*(1/n1+1/n2)]=
=SQRT(54*(1-0.54)*(1/163+1/212))
=0.52
our observed difference p1-p2=0.05
p(Difference>0.09) =1-p(Difference<=0.09)=1-NORM.DIST(.09,.05,.52,TRUE)
=0.469