Simulating confidence intervals. In Exercise 21.19, you found the recipe for a 68% confidence interval for a population proportion p. Suppose that (unknown to anyone) 60% of the voters in her district favor the reelection of Congresswoman Caucus.

(a) How would you simulate the votes of an SRS of 25 voters?

(b) Simulate choosing 10 SRSs, using a different row in Table A for each sample.

What are the 10 values of the sample proportion ^p who favor Caucus?

(c) Find the 68% confidence interval for p from each of your 10 samples.

How many of the intervals capture the true parameter value p = 0.6? (Samples of size 25 are not large enough for our recipe to be very accurate, but even a small simulation illustrates how confidence intervals behave in repeated samples.)