Lecture08

# Lecture08 - How certain are we Lecture 8 Confidence...

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Sociology 549, Paul von Hippel 1 How certain are we? Lecture 8 Confidence intervals  for the mean

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Sociology 549, Paul von Hippel 2 Overview • Review of central limit theorem (CLT) • Turning the CLT around to get  confidence  intervals, e.g. Confidence interval for a mean: We are 95% confident that new sociology BAs (population) have an average starting salary ( parameter ) between \$27,369 and \$30,299 ( interval )
Sociology 549, Paul von Hippel 3 Central limit theorem for the mean:  Review N Y Y Y Y Y / ere wh 96 . 1 in is σ μ = ± The sample mean is usually within a couple standard errors of the population mean. In 95% of all samples, In 99% of all samples, N Y Y Y Y Y / ere wh 58 . 2 in is = ±

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Sociology 549, Paul von Hippel 4 Central limit theorem for the mean:  Using abbreviated normal table N Z Y Y Y Y Y / ere wh in is σ μ = ± The sample mean is usually within a couple standard errors of the population mean. In Confidence% of all samples, where Z comes from the “z (standard normal)…table” +Z - Z Area from -Z to +Z Confidence z 95% 1.96
Sociology 549, Paul von Hippel 5 Central limit theorem for the mean:  So what? If you know the population mean, the central limit theorem helps you guess the sample mean. But in practice you know the sample mean, and want to guess the population mean.

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Sociology 549, Paul von Hippel 6 Turning around the central limit  theorem: Normal confidence interval N Z Y Y Y Y Y / ere wh in is σ μ = ± Central limit theorem : The sample mean is usually within a couple standard errors of the population mean. In Confidence% of all samples, Confidence interval : The population mean is usually within a couple standard errors of the sample mean. We are Confidence% confident that N S S ZS Y Y Y Y Y / ere wh in is = ± hopefully close
Sociology 549, Paul von Hippel 7 Normal confidence interval : Example #1 data • National Association of Colleges and Employers • Sample of  N =92 Sociology BAs, graduating 2000- 01  not a Random Sample but we’ll pretend it is • Variable: starting salary ( Y ) in thousands Cases: 38.0, 28.0, 28.0, 24.6, … 095 . 7 834 . 28 = = Y S Y

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Sociology 549, Paul von Hippel 8 Normal confidence interval: Example #1 calculation If we want 95% confidence, then  Z =1.96. 30.284 and 7.384 2 between is 450 . 1 28.834 in is ) 7397 (. 96 . 1 28.834 in is 7397 . 92 / 095 . 7 e wher 96 . 1 28.834 in is / where in is Y Y Y Y Y Y Y Y Y Y S S N S S ZS Y μ ± ± = = ± = ± Confidence z 95% 1.96
Sociology 549, Paul von Hippel 9 Normal confidence interval:

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Lecture08 - How certain are we Lecture 8 Confidence...

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