Question

In a certain election, 52% of the women voters voted for Candidate A, while only 50% of men voters voted for Candidate A. An exit poll of 300 women and 176 men was conducted. Let p̂ 1p^1 and p̂ 2p^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.

1. What is the expected value of p̂ 1p^1? [Answer to two decimal places.]

2. What is the standard deviation of p̂ 1p^1? [Answer to four decimal places.]

3. What is the expected value of p̂ 2p^2? [Answer to two decimal places.]

4. What is the standard deviation of p̂ 2p^2? [Answer to four decimal places.]

5. What is the expected value of p̂ 1−p̂ 2p^1−p^2? [Answer to two decimal places.]

6. What is the standard deviation of p̂ 1−p̂ 2p^1−p^2? [Answer to four decimal places.]

7. What is the probability that the difference p̂ 1−p̂ 2p^1−p^2 will be larger than 0.05? [Answer to four decimal places.]

Answer 1

1) expected value of p^1 =0.52

2) standard deviation of p^1 =sqrt(p1*(1-p1)/n)=0.0288

3) expected value of p^2 =0.50

4) standard deviation of p^2 =sqrt(p2*(1-p2)/n)=0.0377

5) expected value of p^1−p^2 =0.52-0.50 =0.02

6)

std deviation    Se =

√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2)                                    =

0.0475

7)

probability that the difference will be larger than 0.05 =P(Z>(0.05-0.02)/0.0475)=P(Z>0.63) =0.2643