Question

Researchers are studying populations of two squirrels, the eastern gray and the western gray. For the eastern gray squirrel, about 22 percent of the population weighs over 0.5 kilogram (kg). For the western gray squirrel, about 36 percent of the population weighs over 0.5 kg. A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western)

Answer 1

The sampling distribution of the difference in the proportions between proportion is given by possible values of the difference.

The mean of the difference in sample proportion is; (E) 0.22 - 0.36

Reasons:

The given information are;

Percentage of eastern gray squirrel population weighing over 0.5 kg = 22%

Percentage of western gray squirrel population weighing over 0.5 kg = 36%

Sample size of the eastern gray squirrels = 60

Sample size of the western gray squirrels = 120

Required:

The mean of the sampling distribution of the difference in sample proportions (eastern minus western)

The mean of the difference is given by the difference of the mean.

The mean of the sampling distribution of the difference in the sampling proportion from two populations is; Mean = p₁ - p₂

Where;

p₁ = The proportion of the eastern gray squirrel = 22% = 0.22

p₂ = The proportion of the western gray squirrel = 36% = 0.36

Therefore;

Mean = p₁ - p₂ = 0.22 - 0.36

The correct option is (E) 0.22 - 0.36

Learn more here:

The possible question options obtained online includes;

`(A) \ \sqrt{(0.22 \cdot (0.78))/(120) + (0.36\cdot (0.64))/(60) }`

`(B) \ \sqrt{(0.22 \cdot (0.78))/(60) + (0.36\cdot (0.64))/(120) }`

(C) 60·(0.22) - 120·(0.36)

(D) 0.36 - 0.22

(E) 0.22 - 0.36