Chapter_5

# Chapter_5 - Decision Making for Two Samples Chapter 5...

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Decision Making for Two Samples Chapter 5

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Sections 5-1 through 5-4 2
True Story In the 1980’s, the Hughes Aircraft Co. (HAC) bought cryogenic coolers for their Bradley Fighting Vehicle night vision assemblies from two different vendors: Hughes Aircraft Co. (HAC) Santa Barbara (in-house) BAC (out-of-house) After installation into the Bradley Fighting Vehicles, the HAC coolers seemed to be failing sooner than the BAC coolers How could the engineers determine if there was a significant difference between the mean lives of the HAC coolers and the BAC coolers? 3

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www.rdysales.com www.us-army-info.com Cooler Bradley Fighting Vehicle 4
Chapter 5 Concepts and Notation We want to compare two different populations. We will assume these populations are independent x 11 , x 12 , …, x 1n1 is a random sample of size n 1 from population 1. . μ 1    is the mean of population 1, σ 2 1 is the variance of population 1. x 21 , x 22 , …, x 2n2 is a random sample of size n 2 from population 2. μ 2 is the mean of population 1, σ 2 2 is the variance of population 2. If both populations are not normally distributed, then the conditions of the Central Limit Theorem apply: n σ X Z = Theorem Limit Central n n X V X E X σ μ = = = , ) ( ) ( Recall 2 5

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Chapter 5 Concepts and Notation Θ = μ 1 2 is the difference between the two population means. The variance and standard deviation of Θ are is the difference between the two sample means 2 1 ˆ X X - = Θ ( 29 2 2 2 1 2 1 2 2 2 1 2 1 2 n n n n V σ + = + = = Θ Θ Θ 6
Z The statistic ( 29 ( 29 ( 29 1 , 0 ~ 2 2 2 1 2 1 2 1 2 1 N n n X X Z σ μ + - - - = 7

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Two-sided Hypothesis Tests on the Differences in Population Means , Variances Known Hypothesis test: – H 0 : μ 1 2 = 0 – H 1 : μ 1 2 0 Select α Way #1: Compute z 0 – If z 0 > z α/2 or if If z 0 < - z α/2 , reject H 0 . Way #2: Compute – If if 0 > U or 0 < L, reject H 0 ( 29 2 2 2 1 2 1 0 2 1 0 n n x x z σ + - - = α/2 z α/2 2 2 2 1 2 1 2 2 1 n n z x x L α + - - = 2 2 2 1 2 1 2 2 1 n n z x x U + + - = 8
One-sided Hypothesis Test (upper) on the Differences in Population Means , Variances Known Hypothesis test: – H 0 : μ 1 2 = 0 – H 1 : μ 1 2 > 0 Select α Way #1: Compute z 0 If z 0 > z α reject H 0 . Way #2: Compute If if 0 < L reject H 0 α z 2 2 2 1 2 1 2 1 n n z x x L σ α + - - = ( 29 2 2 2 1 2 1 0 2 1 0 n n x x z + - - = 9

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One-sided Hypothesis Test (lower) on the Differences in Population Means , Variances Known Hypothesis test: – H 0 : μ 1 2 = 0 – H 1 : μ 1 2 < 0 Select α Way #1: Compute z 0 If z 0 < - z α reject H 0 . Way #2: Compute If if 0 > U reject H 0 α z 2 2 2 1 2 1 2 1 n n z x x U σ α + + - = ( 29 2 2 2 1 2 1 0 2 1 0 n n x x z + - - = 10
Summary: Two-Sided Confidence Interval on Population Mean, μ A (1- α29% confidence interval on the true difference between means is given by L and U: L: lower value U: Upper value ( 29 2 2 2 1 2 1 2 2 1 2 2 2 1 2 1 2 2 1 2 1 1 n n z x x U n n z x x L U L P σ α μ + + - = + - - = - = - 11

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Summary: One-Sided Confidence Intervals on Population Mean, μ A (1- α29% confidence interval on the true
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## This note was uploaded on 12/11/2009 for the course CSE IEE taught by Professor Chattin during the Summer '09 term at ASU.

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Chapter_5 - Decision Making for Two Samples Chapter 5...

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