Refer to given Exercise, in which the proportions of obese children in urban and rural areas are to be compared. Random samples of 900 children from each type of area are taken. Suppose that in fact, 20% of the children are obese in both populations.
a. Give numerical values for the mean and standard deviation of the sampling distribution of P^1 - P^2.
b. Suppose that the samples are taken and the difference in sample proportions is 0.05. Find the standardized statistic corresponding to this difference.
c. Draw a picture of the sampling distribution, and illustrate where the difference of 0.05 falls on it.
d. If the population proportions really are equal, is a difference in sample proportions of 0.05 plausible? Explain.
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.
