Question

In​ 2003, an organization surveyed 1 comma 510 adult Americans and asked about a certain​ war, "Do you believe the United States made the right or wrong decision to use military​ force?" Of the 1 comma 510 adult Americans​ surveyed, 1 comma 086 stated the United States made the right decision. In​ 2008, the organization asked the same question of 1 comma 510 adult Americans and found that 573 believed the United States made the right decision. Construct and interpret a​ 90% confidence interval for the difference between the two population​ proportions, p 2003 minus p 2008. The lower bound of a​ 90% confidence interval is nothing. ​(Round to three decimal places as​ needed.) The upper bound of a​ 90% confidence interval is nothing. ​(Round to three decimal places as​ needed.) Interpret the​ 90% confidence interval for the difference between the two population​ proportions, p 2003 minus p 2008. Choose the correct answer below. A. There is​ 90% confidence that the difference in the proportion of adult Americans from 2003 to 2008 who believe the United States made the right decision to use military force in the country is between the lower and upper bounds of the interval. B. There is​ 10% confidence that the difference in the proportion of adult Americans from 2003 to 2008 who believe the United States made the right decision to use military force in the country is between the lower and upper bounds of the interval. C. There is​ 90% confidence that the difference in the proportion of adult Americans from 2003 to 2008 who believe the United States made the right decision to use military force in the country is greater than the lower bound.

Answer 1

Let p1 = p2003 and p2 = p2008

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Lower bound = 0.312

Upper bound = 0.368

Correct option is

A. There is​ 90% confidence that the difference in the proportion of adult Americans from 2003 to 2008 who believe the United States made the right decision to use military force in the country is between the lower and upper bounds of the interval.