For Questions 3 and 4, consider the following scenario:

Cory is serving coffee in a large reception with many guests. There are two kinds of coffee: regular and decaf. So far, he has served 71 cups of regular and 49 cups of decaf.

Question 3.

Based on the information so far:

(a) Estimate the proportion of coffee-drinking guests who prefer regular.

(b) Find the margin of error at 90% confidence.

(c) Construct a 90% confidence interval for the proportion of coffee-drinking guests who prefer regular. (d) Construct a 95% confidence interval for the proportion of coffee-drinking guests who prefer regular.

Question 4.

Cory is wondering whether the coffee-drinking guests are evenly split (i.e., 50%-50%) between their pref- erences for regular and decaf.

(a) Formulate the null and alternative hypotheses that can be used to determine whether the guests are evenly split.

(b) Find the p-value for the hypothesis test.

(c) What should Cory's conclusion be at = 0.05?

(d) What should Cory's conclusion be at = 0.01?