Pew Research found that, in 2013, 50% of American adults favored allowing same-sex couples to marry legally. This is up from 48% in 2012. The 2013 estimate was based on a random sample of 1,501 adults. Assume the same sample size was used in 2012. ["Changing Attitudes on Gay Marriage,” Pew Internet and American Life Project, June 2013.]

1. Compute and interpret a 95% confidence interval for the difference in the proportion of all American adults who favor allowing same-sex couples to marry.

2. What is meant by the phrase “95% confident in this context?
3. Does this interval provide evidence that the proportion of people who favor allowing same
sex couples to marry has increased?
4. Because it is known that support for allowing same-sex couples to marry has been rising, it would be reasonable to perform a one-sided hypothesis test with the alternative hypothesis that the proportion of Americans who favor allowing such marriages is greater in 2013 than 2012. Would such a test cause you to reach the same conclusion you reached in question 3?