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# L26posted - Paired t-test Earlier tested μ 1 = μ 2 using...

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Unformatted text preview: Paired t-test Earlier tested μ 1 = μ 2 using two inde- pendent random samples { X 1 ,...,X n 1 } and { Y 1 ,...,Y n 2 } from N ( μ 1 ,σ 2 1 ) ,N ( μ 2 ,σ 2 2 ) populations. Basis: ¯ X- ¯ Y ∼ 2-sample Z or 2-sample t , depending whether variances were known or not. 1 Variance both populations added. In- crease in “noise” so harder to reject H because As a result, statistical test may not be sensitive to small differences in signal μ 1- μ 2 . Sometimes experiment can be designed in advance to reduce variation in the population by pairing observations and taking differences before analysing. 2 Example 4.6-3, p 267 . Test whether knowl- edge of basic statistical concepts improved af- ter a short course given to engineers. Design 1. Random sample 10 engineers prior to course and test them. Scores { Y 1 ,...,Y 10 } . Take an- other random sample 10 engineers, give them the course, then test them. Scores { X 1 ,...,X 10 } ....
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## This note was uploaded on 01/03/2012 for the course EE 1244 taught by Professor Drera during the Fall '10 term at Conestoga.

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L26posted - Paired t-test Earlier tested μ 1 = μ 2 using...

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