Analyze the possible causes of the change in the percentage of Current Population Survey young-adult respondents who lived with their parents between February and July 2020, focusing on the possibility that it's just sampling variation. Your answer should include the following, all integrated into one paper that makes a clear argument (i.e., your answer should not have question numbers in it):

a) A discussion of what sampling variation is and what it would mean concretely for the difference between the February and July 2020 results to represent "just sampling variation."

b) A discussion of the amount of sampling variation you'd expect in the distribution of sample proportions for samples like these (i.e., samples of about 5000 people, from a population where about 50% of the young adults live with their parents). (Hint: Talk about the standard deviation of the distribution of sample proportions.)

c) An analysis of whether it's likely that the difference between the February and July results represents "just sampling variation."

d) Suggestions about what else besides sampling variation might drive a difference between the February and July samples, and which of those possible reasons you think are likely and why.