Question: In order to get truthful responses to potentially embarrassing questions, researchers often ask the question in conjunction with some other activity. Suppose that a large group of adults are interviewed to determine the proportion that cheated on their income tax. Each person is given a die and placed in a private room. The instructions are as follows: "Roll a die. If you rolled either a 3 or a 4 OR you have ever cheated on your income tax, answer BLUE. Otherwise answer YELLOW."

(A) Suppose that l0% of the people answer YELLOW. What is the approximate proportion of the adults in this survey that have cheated on their income tax?

(B) Suppose that the results from part (A) came from a random sample of 45 adults. What is the 90% confidence interval for the true proportion of adults who have cheated on their income tax?