Question

In​ 2003, an organization surveyed 1,500 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 1,500 adult Americans​ surveyed, 1,080 stated the United States made the right decision. In​ 2008, the organization asked the same question of 1,500 adult Americans and found that 575 believed the United States made the right decision. Construct and interpret a​ 90% confidence interval for the difference between the two population​ proportions, p2003−p2008.

The lower bound of a 90% confidence interval is - (Round to three decimal places as needed.) The upper bound of a 90% confidence interval is (Round to three decimal places as needed.) Interpret the 90% confidence interval for the difference between the two population proportions, P2003 -P2008. Choose the correct answer below. Os. 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 in the confidence interval. OB. 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. OC. 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 in the confidence interval

Answer 1

X1	1080		X2	575
n1	1500		n2	1500
P1	0.72000	X1/n1	P2	0.383333	X2/n2

90% Confidence interval

90% CI	alpha	0.1
Zc	1.644854	Use Z table
ME	0.028107	Zc*SQRT(P1(1-P1)/n1+P2(1-P2)/n2)
Upper	0.364774	(P1-P2) + Zc*SQRT(P1(1-P1)/n1+P2(1-P2)/n2)
Lower	0.30856	(P1-P2) - Zc*SQRT(P1(1-P1)/n1+P2(1-P2)/n2)

Lower bound = 0.309

Upper bound = 0.365

OA 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 in the confidence interval.