The Married variable in ACS codes whether each respondent is married (1) or not (0).
(a) In the ACS dataset, there are 825 people who are 15 years of age or older, and p̂ = 0.53 of these people are married. Generate and interpret a 90% confidence interval for the proportion of US adults aged 15 and older who are married.
(b) While the American Community Survey surveys a sample of US residents every year, the decennial census surveys the entire US population every 10 years. The American Community Survey has been conducted in some form yearly since 1850, and the decennial census has been conducted in years ending in ‘‘0” since 1790, meaning that there have been 17 years of overlap. Suppose we were to use the ACS from each of these 17 years to create a 90% confidence interval for the proportion of people aged 15 and older in the US who were married (as of that year). If there were no sampling bias and everyone responded to the census, approximately how many of these intervals do you think would have contained the true proportion of married adults as obtained by the census?
(c) Based on the 2000 census, 54.5% of people aged 15 and older in the US were married in 2000. Do the data from our ACS sub-sample provide significant evidence that the proportion of people aged 15 and older in the US who were married in 2010 is different than in 2000?

The American Community Survey, administered by the US Census Bureau, is given every year to a random sample of about 3.5 million households (about 3% of all US households). It has been crucial for government and policy decisions, and helps to determine how over 400 billion dollars of government funds are distributed each year. Unfortunately, the House voted in May 2012 to eliminate this valuable source of information. Data on a random sample of 1% of all US residents are made public (after ensuring anonymity), and we have selected a random sub-sample of n = 1000 from the 2010 data, stored in ACS.