We see in the All-Countries dataset that the percent of the population living in rural areas is 8.0 in Argentina and 34.4 in Bolivia. Suppose we take random samples of size 200 from each country, and compute the difference in sample proportions p̂_A − p̂_B, where p̂_A represents the sample proportion living in rural areas in Argentina and p̂_B represents the proportion of the sample that lives in rural areas in Bolivia.
(a) Find the mean and standard deviation of the distribution of differences in sample proportions, p̂_A − p̂_B.
(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 −0.3? Explain.