For a single toss of a coin, let y = 1 for a head and y =
Question:
For a single toss of a coin, let y = 1 for a head and y = 0 for a tail, 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 coin is flipped 10 times, yielding six heads and four tails. Construct the sample data distribution.
(c) Use the applet for the Sampling Distribution for the Sample Proportion at www.artofstat.com/webapps.
html to simulate what would happen if everyone in a university with 10,000 students flipped a coin 10 times and observed the proportion of heads 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).)
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