Joe flips a coin 200 times and records 115 heads.

a) Give a 95% confidence interval for the true proportion of heads that this coin yields using Wald, score, and Wilson methods.

b) Does the confidence interval produced by prop. test() match any of these? If so, which one? (Try prop. test() with correct set to both TRUE and FALSE.) Note that? prop. test does not specify just what method is being used but does reference two 1998 papers that compare multiple methods (seven in one paper, eleven in the other) for computing confidence intervals for a single proportion. If you use uniroot (), be sure to consider the estimated precision when making your comparisons.