For a single roll of a die, let y = 1 for an even number and y = 0 for an odd number, to simulate the vote in an election with two equally preferred candidates.

(a) Construct the probability distribution for y, and find its mean.

(b) The die is rolled 10 times, yielding an even number six times and an odd number four times. Construct the sample data distribution.

(c) Use the applet for the Sampling Distribution for the Sample Proportion at www.pearsonglobaleditions.

com/Agresti to simulate what would happen if everyone in a university with 10,000 students rolled a die 10 times and observed the proportion of times an even number comes up in the sample. Describe the shape and spread of the empirical sampling distribution compared to the distributions in

(a) and (b).

(d) What does the applet report for the mean and the standard deviation of the empirical sampling distribution in (c)? What are the theoretical values for the true sampling distribution? (In finding this, you can use 0.50 as the population standard deviation of the distribution in (a).)