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chap14_2010 - Chapter 14 Single-Population Estimation...

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Chapter 14 Single-Population Estimation
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Population Statistics Population Statistics: μ σ , usually unknown Using Sample Statistics to estimate population statistics: Point estimates Confidence interval 2 ˆ d R = σ k x x = = μ ˆ 4 ˆ c s = σ
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Confidence Interval Wrong Meaning: Probability within the confidence interval is ..% True meaning: The interval will contain the population statistics ..% times
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Confidence Interval for Population Mean Confidence Interval If σ is known, If σ is unknown, n z x n z x σ μ σ α α 2 2 1 - + + n s t x n s t x n n 1 , 1 , 2 2 - - + - α α μ
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Common Confidence Levels Confidence Level 1- α α α /2 1- α /2 90% .90 .10 .05 .95 95% .95 .05 .025 .975 99% .99 .01 .005 .995 z 0.900 1.282 0.950 1.645 0.975 1.960 0.990 2.326 0.995 2.576 0.100 -1.282 0.050 -1.645 0.025 -1.960 0.010 -2.326 0.005 -2.576 1- α α /2 α /2 -z z 1- α α -z
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Example 14.2 σ =350, n=40, 90% CI 95% CI 99% CI n z x n z x σ μ σ α α 2 2 1 - + + 840 = x 40 350 645 . 1 840 40 350 645 . 1 840 + - μ 03 . 931 97 . 748 μ 40 350 960 . 1 840 40 350 960 . 1 840 + - μ 46 . 948 54 . 731 μ 40 350 576 . 2 840 40 350 576 . 2 840 + - μ 55 . 982 45 . 697 μ
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Confidence Interval for Population Mean – Sample size Can be (1- α ) confident that the error will not exceed a specified amount E when sample size is Round up to an integer 2 2 = E z n σ α | | μ - x
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