## Researchers are studying two populations of sea turtles. In population D, 30 percent of the turtles have a shell length greater than 2 feet.

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.

Question 2

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

(c) Can it be assumed that the sampling distribution of the difference of the sample proportions pˆD−pˆE is approximately normal? Justify your answer.

(d) Consider your answer in part (a). What is the probability that pˆD−pˆE is greater than the value found in part (a)? Show your work

## Answers ( )

Answer:a. 0.1917

b. 0.0914

d. 0.1580

Step-by-step explanation:(a)

Mean, = 0.375 -0.1833 =

0.1917(b) sample prop ? Show your work and label each value.

Mean, = = 0.1917

Standard deviation =

Standard deviation =

Standard deviation = 0.0914

(c)

Normality condition:

np ≥ 10 and n(1-p) ≥ 10

Both the samples satisfy the normality condition.

(d)

The probability is obtained by calculating the z score,

= 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