Show all your work. Indicate clearly themethods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

Researchers are studying two populations of sea turtles. In population D, 30 percent of the turtles have a shell length greater than 2 feet. In population E, 20 percent of the turtles have a shell length greater than 2 feet. From a random sample of 40 turtles selected from D, 15 had a shell length greater than 2 feet. From a random sample of 60 turtles selected from E, 11 had a shell length greater than 2 feet. LetpD represent the sample proportion for D, and letpE represent the sample proportion for E.

a) What is the value of the differencepD pE? Show your work.

(b) What are the mean and standard deviation of the sampling distribution of the difference in sample proportionspD pE? Show your work and label each value.

(c) Can it be assumed that the sampling distribution of the difference of the sample proportionspDpEis approximately normal? Justify your answer.

(d) Consider your answer in part (a). What is the probability thatpD pEis greater than the value found in part (a)? Show your work.

P^ represents P-hat.