Overview
On this page, we study the concept of a confidence interval for a population mean and how to find it from a given sample.
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Understand the derivation of a confidence interval for a population mean from the central limit theorem.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
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Be able to construct confidence intervals for a population mean at any confidence level when the population standard deviation is known.
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Understand the correct interpretation of a confidence interval: When repeated often enough, 95 percent of all samples will yield a 95 percent confidence interval that contains the population mean.
To prepare for class
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Watch the following videos (by jbstatistics) which give an introduction to confidence intervals for a parameter and show a detailed example calculation:
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Watch the following video (by Brendan Cordy) which shows a detailed explanation of the formula for the margin of error, and goes through a detailed example calculation:
After class
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Watch the following video (by Brendan Cordy) which clarifies the meaning of the confidence level:
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Play with the following interactive applet to better understand the meaning of a confidence level. The app allows to pick a random sample from a given population and then shows the associated confidence interval for the population mean - by repeating this often enough, you can see how often the confidence interval “misses” (shown in red) the population mean:
https://digitalfirst.bfwpub.com/stats_applet/stats_applet_4_ci.html
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Watch the following videos (by jbstatistics) which explains how to determine the necessary sample size to achieve a given confidence level and margin of error:
