The Gallup organization surveyed 1100 adult Americans on May 6- 9, 2002, and conducted an independent survey of 1100 adult Americans on May 8- 11, 2014. In both surveys they asked the following: "Right now, do you think the state of moral values in the country as a whole is getting better or getting worse?" On May 8- 11,2014, 816 of the 1100 surveyed responded that the state of moral values is getting worse; on May 6- 9,2002,737 of the 1100 surveyed responded that the state of moral values is getting worse. Construct and interpret a \(90 \%\) confidence interval for the difference between the two population proportions.

Approach We can compute a \(90 \%\) confidence interval for the two population proportions provided that the stated requirements are satisfied. We then construct the interval by hand using Formula (3) or using technology.

Formula 3

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2) Lower bound: (1-12) - Za - 2 (1 1), 2(1-2) - n1 + n2 (3) 1(11) 2(1-2) Upper bound: (1 2) + Z * n1 + n2