Lecture 14 - No Instructor Office Hours Today Ajay Malaviya...

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No Instructor Office Hours Today Ajay Malaviya will be available from 1:30- 2:30 today in CII 5208 for Exam 2 Grading Questions. Please briefly prepare your questions in written form before meeting with Ajay.
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Course Project Abstracts due on Friday, April 4, 2008 (same day as exam 3) Abstracts should be brief and to the point: Tentative Project Title and Four Sentences 1. Objective of the study 2. Summary/Source of the data 3. Anticipated method(s) to be applied 4. How the study relates to your major
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Tests of Hypothesis for Two Populations (Moving on to Chapter 9) As more cases are considered, it is important to carefully review the assumptions of any statistical procedure with respect to: Sample Size Variance (known, unknown, etc.) Input Population (Normal vs. non-Normal)
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We also have to carefully consider the design decisions associated with statistical procedures and their tradeoffs including: Type I error – confidence level Sample Size Type II error - sensitivity Precision (e.g., interval width) Variation control strategy (e.g., blocking)
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The difference in two sample means (Xbar-Ybar) from normal input populations where σ values are known , follows a normal distribution with parameters: μ = μ 1 - μ 2 and σ Xbar-Ybar = ( σ 1 2 /m + σ 2 2 /n) 1/2
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For tests on the difference in two population means ( μ 1 - μ 2 ) from normal input populations where σ values are known , the test statistic is given by: Z = (Xbar-Ybar-( μ 1 - μ 2 )) / ( σ 1 2 /m + σ 2 2 /n) 1/2 vs. Z α or Z α /2
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For tests on the difference in two population means with normal input populations and known σ , the type II error probability is estimated using: (see page 330 of the text) Upper tail test: Ha: μ 1 - μ 2 > Δ 0 β ( Δ ’) = Ф {Z α -( Δ ’- Δ 0 )/ σ } Lower tail test: H a : μ 1 - μ 2 < Δ 0 β ( Δ ’) = 1 - Ф {-Z α Δ ’- Δ 0 )/ σ } Two tail test: H a : μ 1 - μ 2 ≠Δ 0 β ( Δ ’) = Ф {Z α /2 Δ ’- Δ 0 )/ σ } - Ф {-Z α /2 Δ ’- Δ 0 )/ σ } where σ = ( σ 1 2 /m + σ 2 2 /n) 1/2
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For tests on the difference in two population means with normal input populations and known σ , the sample size for which a level α test also has β ( Δ ’)= β can be estimated when
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Lecture 14 - No Instructor Office Hours Today Ajay Malaviya...

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