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In​ 2003, an organization surveyed 1 comma 500 adult Americans and asked about a certain​ war,...

In​ 2003, an organization surveyed 1 comma 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 comma 500 adult Americans​ surveyed, 1 comma 090 stated the United States made the right decision. In​ 2008, the organization asked the same question of 1 comma 500 adult Americans and found that 570 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.

A. The lower bound of a 90% confidence interval is...

B. The upper bound of a 90% confidence interval is...

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Answer #1

Here, , n1 = 1500 , n2 = 1500
p1cap = 0.7267 , p2cap = 0.38


Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.7267 * (1-0.7267)/1500 + 0.38*(1-0.38)/1500)
SE = 0.017

For 0.9 CI, z-value = 1.64
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.7267 - 0.38 - 1.64*0.017, 0.7267 - 0.38 + 1.64*0.017)
CI = (0.3188 , 0.3746)


Lower bound = 0.3188
Upper bound = 0.3746

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