We see in the All-Countries dataset that the percent of the population that is over 65 is 13.4 in Australia and 12.5 in New Zealand. Suppose we take random samples of size 500 from Australia and size 300 from New Zealand, and compute the difference in sample proportions p̂_A − p̂_NZ, where p̂_A represents the sample proportion of elderly in Australia and p̂_NZ represents the sample proportion of elderly in New Zealand. Find the mean and standard deviation of the differences in sample proportions.