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Unformatted text preview: 6.1 Estimating with Confidence give Test Y to an SRS of 400 students, x = 500 What can you say about the mean score in population? x is an unbiased estimator of ( x = ) but how reliable is this estimate? (how variable is the statistic?) recall x is approximately N (, n ) when n is large suppose population standard deviation = 100, then x = n = 400 100 = 5 (unrealistic to assume we would know - relax this assumption in Chapter 7) x has normal distribution centered at unknown population mean with x = 5 Confidence intervals the 68-95-99.7 rule says that, for any N distribution, 95% of observations within 2 sd of mean 95% chance x will be within 2 standard deviations of x 95% chance x will be within 10 points of population mean to say that x lies within 10 points of is the same as saying that is within 10 points of x so 95% of all samples will capture the true in the interval from x- 10 to x + 10 our sample gave x = 500 95% confidence interval= x 10 500 10 [490, 510] we say that we are 95% confident that the unknown mean score lies between [490, 510] Once we look at a sample and construct a confidence interval, there are two possibilities: 1) The interval between 490 and 510 contains the true population mean . Our sample is one of the 95% of samples where lies within 10 points of x . 2) The true population mean is not contained between 490 and 510 (rare result)....
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- Fall '08