Overview
On this page, we discuss the concept of a “Hypothesis Test” to infer information from given sample data, especially for a population mean.
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 general concept of a Hypothesis Test, the definition of the Null Hypothesis \(H_0\) and Alternative Hypothesis \(H_a\), and how a certain probability (the “P-value”) can be used to decide whether or not to “reject” \(H_0\).
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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Apply the general concept in the special case of a Hypothesis Test on a Population Mean, either when the population standard deviation \(\sigma\) is known (a \(z\)-test) or unknown (a \(t\)-test).
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Understand the meaning of the significance level for a Hypothesis Test.
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Be aware of the importance of clear conclusions: The result of a Hypothesis Test should always be either to reject \(H_0\) or do not reject \(H_0\).
To prepare for class
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Watch the following video (10min, by jbstatistics) which introduces the general principle of a Hypothesis Test:
After class
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Watch the following video (11min, by jbstatistics) which shows how to do a Hypothesis Test for a population mean when the population standard deviation \(\sigma\) is known (a so-called \(z\)-test):
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Watch the following video (10min, by jbstatistics) which explains how to find the \(P\)-value for a \(z\)-test, and the meaning of the significance level:
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Watch the following video (7min, by jbstatistics) which explains how to decide whether to use a \(z\)- or \(t\)-test for a population mean:
