A random sample of 250 observations is taken from population A, which has 30% of its population living in poverty: πA = .3. A second random sample of size 350 is taken independently taken from population B, which has 15% of its population living in poverty: πB = .15.
a. What are the mean and standard deviation of the difference in the sample proportions, A – B?
b. Describe the shape of the sampling distribution of the difference in the sample proportions, A – B?
c. Is it appropriate to use the normal approximation to the sampling distribution of the difference in the sample proportions, A – B?