week2 - Econ 508 Discussion 4 Feb 2011 Juan Fung 1 Condence...

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Econ 508: Discussion 4 Feb. 2011 Juan Fung 1 Confidence intervals and hypothesis testing for μ and σ 2 This is a quick review. By now, you should be very comfortable with this. It might be useful to review the important sampling distributions from Econ 506: N, t, χ 2 , and F . If you don’t observe population mean and variance, but do have an IID normal sample, you can easily estimate the mean and variance, and characterize their distributions. This allows you to construct test statistics (or confidence intervals)! The test statistics depend on which parameters you’re testing, and on which you know. 1. Consider a sample of 64 SAT math scores, with sample mean 520 and standard devi- ation 100. Find a 95% confidence interval for the true mean. At the 5% level, would you reject the hypothesis H 0 : μ = 500? Find critical value t . 025 , 63 2 . 30 (why t ?). Then the 95% CI is given by 520 ± 2 . 3( 100 8 ) = 520 ± 32 . 5 = (487 . 5 , 552 . 5) . Since 500 is in the CI, fail to reject H 0 (easily compute the test statistic to verify).
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