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 pDrepresent 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 approximately normal? Justify your answer.
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 pDrepresent 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 approximately normal? Justify your answer.
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