Question

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 085 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. 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? 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. B. 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. 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 between the lower and upper bounds of the interval.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary confidence interval:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions

90% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	1085	1500	570	1500	0.34333333	0.017043517	0.31529924	0.37136742

Hence,

90% confidence interval will be:

Lower bound = 0.315

Upper bound = 0.371

Interpretation: Option C is correct.