The All-Countries dataset shows that the percent of the population living in rural areas is 57.3% in Egypt and 21.6% in Jordan. Suppose we take random samples of size 400 people from each country, and compute the difference in sample proportions p̂_E − p̂_J, where p̂_E represents the sample proportion living in rural areas in Egypt and p̂_J represents the sample proportion living in rural areas in Jordan.
(a) Find the mean and standard deviation of the distribution of differences in sample proportions, p̂_E − p̂_J.
(b) If the sample sizes are large enough for the Central Limit Theorem to apply, draw a curve showing the shape of the sampling distribution. Include at least three values on the horizontal axis.
(c) Using the graph drawn in part (b), are we likely to see a difference in sample proportions as large in magnitude as 0.4? As large as 0.5? Explain.