There is some evidence that women tend to vote earlier in the day and men tend to vote later in the day. If men and women vote differently, then exit polls taken early in the day may not reflect the eventual results. Suppose that in a particular election, 51% of the voters who vote in the morning vote for Candidate A, while only 48% of those who vote later vote for Candidate A. An exit poll is based on 500 voters in the morning and 500 voters later in the day. Define P^1 to be the proportion of the morning sample that voted for Candidate A and P^2 to be the proportion of the later sample that voted for Candidate A.
a. Based on the morning voters only, describe the sampling distribution of P^1. Draw a figure similar to given Figure 1.
b. What is the mean of the sampling distribution of P^1 - P^2?
c. What is the standard deviation of the sampling distribution of P^1 - P^2?
d. Draw a picture of the sampling distribution of P^1 - P^2, similar to given Figure 2.
e. Using the figure you drew in part (d), sketch the region of the figure that corresponds to having samples with P^1 being less than P^2.
f. Using your knowledge of how to find areas under normal curves from Chapter 8, find the probability that P^1 - P^2, P^1) than later in the day (P^2).
