The National Association of Realtors (NAR) reported the results of an April 2015 survey of home buyers. In a random sample of 1,971 residential properties purchased during the year, 414 were purchased as a vacation home. Five years ago, 10% of residential properties were vacation homes.
a. Do the survey results allow the NAR to conclude (at α = .01) that the percentage of all residential properties purchased for vacation homes is greater than 10%?
b. In a previous year, the NAR sent the survey questionnaire to a nationwide sample of 45,000 new home owners, of which 1,982 responded to the survey. How might this bias the results?