# ch12 - Ch 12 Example1)SEofpercentages (s)...

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1 Ch 12 The Accuracy of Percentage • Example 1) SE of percentages • Politicians would participate in an election only if  (s)he has a chance of winning. • Assume a village with 100,000 eligible voters. • A student in “Statistics for Economists” is hired and a  sample of 2,500 voters is surveyed. • In the sample 1,328 (53%) favor the politician. • Should the politician participate in the upcoming  elections? How far wrong is the estimate likely to be?

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2 • To get the SE for the sum, we need the SD of the  box ??? 0 ??? ’ s 1 ’ s 100, 000 Ti cket s 2, 500 Dr aws ) s 0' of fraction ( ) s 1' of fraction ( × • But, now we are stuck! We can’t calculate the SE as  we don’t know ???, i.e. the fractions of 1’s and 0’s
3 The Bootstrap Survey organizations go around this obstacle with the  bootstrap . Substitute the fractions observed in the sample for the  unknown fractions in the box. 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 is 50 . 0 47 . 0 53 . 0 × The SE for the number of voters favoring the candidate is 25 50 . 0 2500 ×

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4 • 25 is the likely size of the chance error in the 1,328  voters that favor the candidate. • 25 people out of 2,500 (the sample size) is 1%. • The SE for percentage of voters in the sample
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ch12 - Ch 12 Example1)SEofpercentages (s)...

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