Population 1. 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 researchers 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 researchers 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. 4. Graph
.2 0 -5 .05 Density .1 .15
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Statistical Significance Any legitimate voting system should be normally distributed because the number of people who vote and the way in which they vote are completely with random regards to statistics. Therefore, according to the Central Limit Theorem which states that a statistical compilation of random observations will be normally distributed, difference between the fraction of the people who voted for Buchanan on Election Day and via absentee ballots would be normally distributed. The z-score tells us the number of standard deviations the observations is from the mean, so it is important in this regard because it allows us to look at the trend of the voting, like which counties Buchanan received large amounts of votes compared to other counties. It would appear that the number of votes Buchanan received in Palm Beach County is too large to have happened by pure chance because the z-score is 22, meaning this observation is 22 standard deviations from the mean. Typically, z-scores do not go above 4. Causal Significance It would appear that the number of votes Buchanan received in Palm Beach County is too large to have happened by pure chance because the z-score is 22, meaning this observation is 22 standard deviations from the mean. Typically, z-scores do not go above 4. Substantive Significance The number of people that mistakenly voted for Buchanan may be around 955. If the difference is truly too large to have happened by chance, this fact is important from an electoral point of view because it presents a flaw in the voting system. Not only should intended votes go to the intended candidate, the number of mistaken votes may have pushed Gore over the top in Florida, giving him the election.