Chapter_5

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

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Decision Making for Two Samples Chapter 5
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sections 5-1 through 5-4 2
Background image of page 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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
www.rdysales.com www.us-army-info.com Cooler Bradley Fighting Vehicle 4
Background image of page 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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Summary: One-Sided Confidence Intervals on Population Mean, μ A (1- α29% confidence interval on the true
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/11/2009 for the course CSE IEE taught by Professor Chattin during the Summer '09 term at ASU.

Page1 / 84

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

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online