Similar to humans, it has been shown that dogs have a "handedness," preferring to use either a right paw or a left paw for certain tasks. Suppose that, in a random sample of 200 beagles, 55 were found to be left-pawed. In another random sample of 200 collies, 40 were found to be left-pawed. Calculate a 95% confidence interval on p1 - p2, where p1 is the proportion of beagles who are left-pawed and p2 is the proportion of collies who are left-pawed. Make sure to show all of the intermediate calculations needed for this result.
(b) Suppose that the margin of error in the previous confidence interval was too large to be of much use. What sample sizes would be necessary to obtain a margin of error no greater than 0.06 (still using a 95% confidence level)? Assume equal sample sizes (n = 12).