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Unformatted text preview: &¡¢£¢ ¤¥ &¦§¨©ª¨«¬­®«¯­¦°± ¡­²³©ª­´µ 7.1. The margin of error in estimation provides a practical upper bound to the difference between a particular estimate and the parameter that it estimates. In this chapter, the margin of error, whenever the confidence level is not explicitly specified, is 1.96*(standard error of the estimator) 7.2. For the estimate of μ given as _ x , the margin of error is 1.96 n x σ σ 96 . 1 = . a . 620 . 40 2 96 . 1 = b . 186 . 100 9 . 96 . 1 = c . 960 . 50 12 96 . 1 = 7.4. A 95% confidence internal for the population mean μ is given by where & can be estimated with the sample standard deviation s for large values of n . a . 604 . 1 . 13 36 42 . 3 96 . 1 1 . 13 ± & ± or 12.496 < μ < 13.704 b . 079 . 73 . 2 64 1047 . 96 . 1 73 . 2 ± & ± or 2.651 < μ < 2.809 c . 320 . 6 . 28 41 09 . 1 96 . 1 6 . 28 ± & ± or 28.280 < μ < 28.920 Intervals constructed in this manner will enclose the true value of μ 95% of the time in repeated sampling. Hence, we are fairly confident that these particular intervals will contain μ . 7.13. For this exercise, n = 32, _ x =11.7 and s = 2.1. The approximate 90% confidence interval for μ , the mean of the population of forecasts all economic forecasters, is 611 . 7 . 11 32 1 . 2 645 . 1 7 . 11 05 ....
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This note was uploaded on 10/02/2009 for the course PSTAT 5E taught by Professor Eduardomontoya during the Spring '08 term at UCSB.

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