In a certain election, 49% of the women voters voted for Candidate A, while only
ID: 3366103 • Letter: I
Question
In a certain election, 49% of the women voters voted for Candidate A, while only 42% of men voters voted for Candidate A. An exit poll of 176 women and 269 men was conducted. Let [^(p)]1 and [^(p)]2denote 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 [^(p)]1? [Answer to two decimal places.]
2. What is the standard deviation of [^(p)]1? [Answer to four decimal places.]
3.What is the expected value of [^(p)]2? [Answer to two decimal places.]
4.What is the standard deviation of [^(p)]2? [Answer to four decimal places.]
5.What is the expected value of [^(p)]1 ? [^(p)]2? [Answer to two decimal places.]
6.What is the standard deviation of [^(p)]1 ? [^(p)]2? [Answer to four decimal places.]
7. What is the probability that the difference [^(p)]1 ? [^(p)]2 will be larger than 0.0799999999999999? [Answer to four decimal places.]
Incorrect. Tries 1/5 Previous TriesExplanation / Answer
1. E(P1) = 0.49
2. SD(P1) = sqrt(0.49*0.51/176) = 0.03768
3. E(P2) = 0.42
4. SD(P2) = sqrt(0.42*0.58/269) = 0.0301
5. E(P1 - P2) = E(P1) - E(P2) = 0.49-0.42 = 0.07
6. SD(p1-p2) = sqrt(var(P1-P2)) = sqrt( 0.037682 +0.03012)
=0.04822
7. P(p1 - p2 > 0.07999) = P(Z > 0.07999 - 0.07 / 0.04822) = P(Z > 0.2072) = 0.41794