A psychologist takes an SRS of 404040 people in their twenties and 606060 people in their fifties and surveys them about their a
nxieties. Suppose that 48\%48%48, percent of people in their twenties and 28\%28%28, percent of people in their fifties have anxiety about flying. The psychologist will then look at the difference (\text{20's}-\text{50's})(20’s−50’s)left parenthesis, start text, 20, apostrophe, s, end text, minus, start text, 50, apostrophe, s, end text, right parenthesis between the proportions of people with anxiety about flying in each sample. What will be the shape of the sampling distribution of the difference in sample proportions, and why?
Answer: Approximately normal, because we expect 19.2 successes and 20.8 failures from people in their twenties, and 16.8 and 43.2 from people in their fifties, and all of these counts are at least 10.
