On June 4-24, 2007, the Gallup Poll asked a random sample of adult Americans abo

Question

On June 4-24, 2007, the Gallup Poll asked a random sample of adult Americans about their attitudes toward interracial marriage. Of the 688 adults interviewed, 77% said they approve of marriage between whites and blacks. In a similar study conducted fifteen years earlier in 1992, 72% said they approve of such a marriage. (Assume that the sample size in 1992 was the same as in 2007.)

a. Do these studies make use of random sampling or random assignment? (No explanation is necessary.) Random sampling

b. Determine a 95% confidence interval for the difference in population proportions who approve of such marriages between 1992 and 2007.

c. Comment on what you can discern from this interval about whether, and if so how, this proportion has changed over that fifteen-year period.

Explanation / Answer

Difference = p (1) - p (2)
Estimate for difference: 0.05
95% CI for difference: (-0.0706135, 0.170613)
Test for difference = 0 (vs not = 0): Z = 0.81 P-Value = 0.417

Fisher's exact test: P-Value = 0.517

P value greater than the significance level , hence we do not reject the hypothesis.

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