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Unformatted text preview: Chapter 12 The Accuracy of Percentages Reasonably, a politician would participate in an election only if (s)he has a chance of winning. Assume a village has 100,000 eligible voters. A student is then hired and a sample of 2,500 voters is surveyed. In the sample it was found that 1,328 (53%) favor the politician. The question now is whether the politician should participate in the upcoming elections. How far wrong is the estimate likely to be? From the sample, it is reasonable to argue that indeed (53%) of the voters favor the politician. However, there is always the possibility of a chance error. To measure this, we need the standard error, which can be calculated by the SE of the percentage of SE of sum n × 100%. the problem is that we cannot calculate the SE of the sum because we do not the standard deviation of the box. Are we stuck? No. What we do is to estimate the standard deviation of the box using the standard deviation of the sample. This is known as bootstrapping . In our example we have 0.53 favored the politician and 0.47 opposed, i.e. 0.53 of 100,000 tickets are marked 1’s and 0.47 of 100,000 tickets are marked 0’s. On this basis, the SD of the box can be estimated by the SD of the sample which is about 0.5. 1 And using this, the SE for the number of voters favoring the candidate is calculated to be 25, which means the 1 strictly speaking we should use the sample standard deviation...
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This note was uploaded on 03/14/2010 for the course ECON Statistics taught by Professor Yy during the Spring '10 term at Seoul National.
- Spring '10