Refer to Exercise, including the information given in part (c). Which of the following could be specified before the samples are taken? Explain.

a. The value of the mean of the sampling distribution of P^{^}₁ - P^{^}₂.

b. The approximate shape of the sampling distribution of P^{^}₁ - P^{^}₂.

c. The standard deviation of the sampling distribution of P^{^}₁ - P^{^}₂.

d. The standard error of the sampling distribution of P^{^}₁ - P^{^}₂.

Exercise
Researchers would like to know whether the proportions of elementary school children who are obese differ in rural and urban areas. They plan to take random samples of 900 children from urban areas and 900 children from rural areas and compare the proportions that are obese. Define Population 1 to be elementary school children in urban areas and Population 2 to be elementary school children in rural areas.

a. Define in words what the parameter p₁ represents in this situation.

b. Define in words what P^{^}₁ is in this situation.

c. Suppose that, unknown to the researchers, p₁ and p₂ are both .20 (20%). Describe the sampling distribution of P^{^}₁ - P^{^}₂, including its mean, standard deviation, and shape.

d. Draw a picture of the sampling distribution that you described in part (c), similar to given Figure.