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 pˆD represent the sample proportion for D, and let pˆE represent the sample proportion for E.

What is the probability that pˆD-pˆE is greater than 0.1917?

Question

Mathematics

Edith Gentry

28 August, 03:50

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 pˆD represent the sample proportion for D, and let pˆE represent the sample proportion for E.

What is the probability that pˆD-pˆE is greater than 0.1917?

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Answers (1)

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Juliana Hicks · Answer 1

Step-by-step explanation:

The probability is obtained by calculating the z score,

(pˆD-pˆE) - (PD - PE)

0.0914

10.1917-0.1

0.0914 = 1.0029

P (z > 1.0029) = 1 - P (z ≤ 1.0029)

The probability is obtained from the z distribution table,

P (Z > 1.0029) = 1-0.8420 = 0.1580