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# Pew Research found that, in 2013, 50% of American adults favored allowing same-sex couples to marry ...

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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.]

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.
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## Stats: Modeling the World

Edition: 4th
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2 weeks ago

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2 weeks ago
 Brilliant
wrote...
2 weeks ago
 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.]What is meant by the phrase "95% confident" in this context?
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2 weeks ago
 If we were to select many pairs of samples of 1501 adults from 2012 and of 1501 adults from 2013 and compute a confidence interval for each pair of samples for the difference in proportions of all American adults in each year who favored allowing same-sex couples to marry, we would expect to capture the actual difference in proportions in the populations in about 95% of the intervals constructed.
wrote...
2 weeks ago
 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.]Does this interval provide evidence that the proportion of people who favor allowing same-sex couples to marry has increased?
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2 weeks ago
 No, a difference of zero is in the interval, so it is plausible that there is no difference in the proportion of American adults who favored allowing same-sex couples to marry in those two years.
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2 weeks ago
 This helped my grade so much
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2 weeks ago
wrote...
2 weeks ago
 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.]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?
wrote...
2 weeks ago
 Yes. Even with a one-sided test, the P-value is 0.12. There is not enough evidence, based on this pair of samples, to conclude that the proportion of all American adults who favored allowing same-sex couples to marry increased from 2012 to 2013.
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