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# handout_6_1 - 6.1 Estimating with Confidence those who took...

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6.1 Estimating with Confidence those who took the SAT math in 2003: mean= 519, sd= 115 give test to SRS of 500 California students: x = 461 (math) What can you say about the mean score μ in population of 385,000? 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 σ = 100, then x = 4.5 (unrealistic to assume we would know σ- CH 7) x has normal distribution centered at unknown population mean μ with x = 4.5 Figure 6.2 •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 9 points of population mean μ •to say that x lies within 9 points of μ is the same as saying that μ is within 9 points of x •so 95% of all samples will capture the true μ in the interval from x - 9 to x + 9 our sample gave x = 461 95% confidence interval= x ± 9 461 ± 9 [452, 470] we say that we are 95% confident that the unknown mean score lies between [452, 470]

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our sample gave x = 461 95% confidence interval= x ± 9 461 ± 9 [452, 470] we say that we are 95% confident that the unknown mean score lies between [452, 470] Once we look at a sample and construct a confidence interval, there are two possibilities: 1) The interval between 452 and 470 contains the true population mean μ Our sample is one of the 95% of samples where μ lies within 9 points of x . 2) The true population mean μ is not contained between 452 and 470 (rare result).
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handout_6_1 - 6.1 Estimating with Confidence those who took...

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