According to the 2006 Australia Census,43 25.5% of Australian women over the age of 25 had a college degree, while the percentage for Australian men was 21.4%. Suppose we select random samples of 200 women and 200 men from this population and look at the differences in proportions with college degrees, p̂_f − p̂_m, in those samples.
(a) Describe the distribution (center, spread, shape) for the difference in sample proportions. Include a rough sketch of the distribution with values labeled on the horizontal axis.
(b) What is the chance that the proportion with college degrees in the men’s sample is actually more than the proportion in the women’s sample?