SOLUTION: Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually

Question 1033601: Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they feel about the President�s handling of the crisis in the financial markets. The results show that 575 out of the 1280 people polled say they either �approve� or �strongly approve� of the President�s handling of this matter. Based on the sample referenced above, find a 95% confidence interval estimate for the proportion of the entire voter population who �approve� or �strongly approve� of the President�s handling of the crisis in the financial markets.
Now, here�s an interesting twist. If the same sample proportion was found in a sample twice as large�that is, 1150 out of 2560�how would this affect the confidence interval?

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The sample mean is 575 / 1280 = 0.449 approx 0.45
:
The sample standard deviation is square root(0.45*0.55/1280) = 0.0139 approx 0.01
:
95% lower = 0.45 - (0.01 * 1.96) = 0.4304 approx 0.43
95% higher = 0.45 + (0.01 * 1.96) = 0.4696 approx 0.47
:
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95% CI = (0.43, 0.47)
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:
The new sample mean is 1150 / 2560 = 0.4492 approx 0.45
:
The new sample standard deviation is square root(0.45*0.55/2560) = 0.0098 approx 0.01
:
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The new 95% CI is the same
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