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February 12, 2009 marked the anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 randomly selected American adults about their education level and their beliefs about the theory of evolution. In their sample, 325 of their respondents had some college education and 228 were college graduates. Among the 325 respondents with some college education, 133 said that they believed in the theory of evolution. Among the 228 respondents who were college graduates, 121 said that they believed in the theory of evolution.
-Construct a 90% confidence interval for the difference between the proportions of college graduates and individuals with some college who believe in the theory of evolution. Round your sample proportions and margin of error to three decimal places.
A) 0.052 to 0.192
B) 0.038 to 0.206
C) 0.079 to 0.165
D) 0.012 to 0.232

Question

Quizplus · Accepted Answer

The sample proportions are 121/228 = 0.531 for college graduates and 133/325 = 0.409 for some college. The difference in proportions is 0.531 - 0.409 = 0.122. Using a standard formula for the confidence interval for the difference in proportions, the margin of error is calculated, resulting in a 90% confidence interval of 0.052 to 0.192.

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