Question 961675: An opinion poll was to be conducted in order to determine how well a particular congressional incumbent was doing at is job. The was the first poll to be conducted on this incumbent, so, the pollsters had no record to go on for past performance. The question to be asked is "Do you approve of the job congressperson smith is doing while in office?" The answer is a simple "yes" or "no." At the 99% level of confidence, what minimum sample size isnecessary to be to sure that the poll is within 2.5% of the population proportion of those that would answer "yes" to this question?
the answer is 2654 but how do I figure this out?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 1) We expect 50% of the voters to support the candidate with a 2.5% confidence interval.
2) The confidence level is written as a Z-score, which is the number of standard deviations away from the mean the range includes. A confidence level of 99 percent includes 2.58 standard deviations on either side of the mean, so the Z-score would be 2.58. This means that there is a 99 percent chance that the actual proportion is within 2.58 standard deviations on either side of the question result.
3) We use .50 as the proportion for the results of this question.
4) Now we can use the following equation
sample size = (Z^2 * P * (1-P)) / C^2, where Z=2.58, P=.50, C=.025
sample size = (2.58^2 *.50 * (.50)) / .025^2 = 2662.56
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