On June 4-24, 2007, the Gallup Poll asked a random sample of adult Americans about their attitudes toward interracial marriage. Of the 2388 adults interviewed, $77 \%$ said they approve of marriage between whites and blacks. In a similar study conducted five years earlier in 2002, 65\% said they approve of such a marriage. (Assume that the sample size in 2002 was the same as in 2007.)
a. Do these studies make use of random sampling or random assignment? (No explanation is necessary.)
b. Determine a $95 \%$ confidence interval for the difference in population proportions who approve of such marriages between 2002 and 2007.
c. Comment on what you can discern from this interval about whether, and if so how, this proportion has changed over that five-year period.

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The Answer of On June 4-24, 2007, the Gallup Poll asked a random sample of adult Americans about their attitudes toward interracial marriage. Of the 2388 adults interviewed, $77 \%$ said they approve of marriage between whites and blacks. In a similar study conducted five years earlier in 2002, 65\% said they approve of such a marriage. (Assume that the sample size in 2002 was the same as in 2007.)
a. Do these studies make use of random sampling or random assignment? (No explanation is necessary.)
b. Determine a $95 \%$ confidence interval for the difference in population proportions who approve of such marriages between 2002 and 2007.
c. Comment on what you can discern from this interval about whether, and if so how, this proportion has changed over that five-year period.

On June 4-24, 2007, the Gallup Poll Asked a Random 77%77 \%77%

On June 4-24, 2007, the Gallup Poll Asked a Random $77 \%$