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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.]

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.
Textbook 

Stats: Modeling the World


Edition: 4th
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2 weeks ago
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Randomization Condition: The adults in the sample were randomly selected by the in both years.
* 10% Condition: The number of American adults was greater than 15,010 (10 x 1,501) in both years.
* Independent samples condition: The two groups are independent of each other because the samples were selected at random.
* Success/Failure Condition: In 2013, 0.50 x 1,501 = 750.5 is the number of successes and the number of failures. In 2012, 0.48 x 1,501 = 720.48 successes and 780.52 failures. The observed number of both successes and failures in both years is larger than 10.

Because the conditions are satisfied, we can model the sampling distribution of the difference in proportions with a Normal model.

n2013 = 1501, 2013 = 0.50, n2012 = 1501, 2012 = 0.48
We estimate SD(2013 - 2012) as
SE(2013 - 2012) = = = 0.018
ME = z* × SE(2013 - 2012) = 1.96(0.018) = 0.036
The observed difference in sample proportions is 0.48 – 0.50 = 0.02, so the 95% confidence interval is 0.02 ± 0.036 = (-0.016,0.056)
We are 95% confident that the true difference in between the proportion of all American adults in 2013 who favored allowing same-sex couples to marry and the proportion of all American adults in 2012 who favored allowing same-sex couples to marry is between -0.016 and 0.056.
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wrote...
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?
wrote...
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?
wrote...
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.
wrote...
2 weeks ago
This helped my grade so much
wrote...
2 weeks ago
Perfect
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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