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# hw - 1 Population 1 n = xbar = 25000 SD = 6000 Population 2...

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1. Population 1 : n = ? ; xbar = 25000 ; SD = 6000 Population 2 : n = ? ; xbar = 28000 ; SD = 9000 What is the 95% confidence interval for the difference? I do not have the n (the number of observations), and I need that value in order to calculate the Confidence Interval. The Confidence interval asks that I multiply the 95% coefficient of 1.96 by the Standard Error. To calculate the Standard Error, I must divide the Standard Deviations by the number of observations, respectively. 2. Population 1 : n = 100 ; xbar = .57 ; SD = (1-0)√(.57)(.43) = .495 Population 2 : n = 100 ; xbar = .32 ; SD = (1-0)√(.32)(.68) = .466 What is the 95% Confidence Interval for the difference? Xbar (1-2) = .57 - .32 = .25 SE (1-2) = √[(.245/100) + (.217/100) = .068 CI(95) = .25 +/- 1.96(.068) = .25 +/- .13 3. Population 1 : n = 70 ; xbar = .26 ; SD = .11 Population 2 : n = 148 ; xbar = .23 ; SD = .13 Can I be 95% confident the researcher’s theory is correct? Xbar(1-2) = .26 - .23 = .03 SE (1-2) = √[(.012/70) + (.017/148) = √.00017 + .00011 = .017 CI(95) = .03 +/- 1.96(.017) = .03 +/- .033 No. I cannot be 955 confident that the researcher’s theory is correct because the confidence interval contains 0 within its range, meaning that it is possible that having your name at the top of the ballot has no effect on the candidates’ chances of winning.

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