Show all your work. Indicate clearly the methods 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. Let PD
represent the sample proportion for D, and let PE represent the sample proportion for E.

(a) What is the value of the difference PD - PE? Show your work

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

(c) Can it be assumed that the sampling distribution of the difference of the sample proportions PD - PE is it approximately normal? Justify your answer.

(d) Consider your answer in part (a). What is the probability that PD - PE is greater than the value found in part (a)? Show your work.