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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 μ in population? • x is an unbiased estimator of μ ( x μ = μ) • but how reliable is this estimate? (how variable is the statistic?) recall x is approximately N (μ, n σ ) when n is large suppose population standard deviation σ = 100, then x σ = n σ = 400 100 = 5 (unrealistic to assume we would know σ relax this assumption in Chapter 7) x has normal distribution centered at unknown population mean μ with x σ = 5 Confidence intervals •the 689599.7 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 μ •95% chance→ x will be within 10 points of population mean μ •to say that x lies within 10 points of μ is the same as saying that μ is within 10 points of x •so 95% of all samples will capture the true μ 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 μ. Our sample is one of the 95% of samples where μ lies within 10 points of x . 2) The true population mean μ is not contained between 490 and 510 (rare result)....
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 Fall '08
 ABDUS,S.
 Normal Distribution, Standard Deviation, researcher, $2000, 1.645 90%

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