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 580 believed the United States made the right decision Construct and interpreta 90% confidence interval for the difference between the two population proportions, Pro-P2008 The lower bound of a 90% confidence intervalis (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, Pacos 2008 Choose the correct answer below OA. There is 30% confidence that the difference in the proportion of adut Americans from 2009 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 OB. There is 80% 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 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 between the lower and upper bounds of the interval lower bound

Answer 1

Answer:

Given,

sample proportion p1^ = x1/n1 = 1080/1500 = 0.72

p2^ = 580/1500 = 0.3867

Pooled proportion p = (x1+x2)/(n1+n2) = (580+1080)/(1500+1500) = 0.5533

Here at 90% CI, z value is 1.645

90% CI = (p1^ - p2^) +/- z*sqrt(p(1-p)(1/n1 + 1/n2))

= (0.72 - 0.3867) +/- 1.645*sqrt(0.5533(1-0.5533)(1/1500 + 1/1500))

= 0.3333 +/- 0.0299

= (0.3034 , 0.3632)

Lower bound = 0.3034

Upper bound = 0.3632