Lecture08

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

This preview shows pages 1–9. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 σ 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 σ σ σ μ = ±

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 σ 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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 σ 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 = ± μ 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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Sociology 549, Paul von Hippel 8 Normal confidence interval: Example #1 calculation If we want 95% confidence, then  Z =1.96.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern