This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 9. Inferences based on two samples Extend confidence interval and hypotheses testing for single mean, proportion, variance to two different means, proportions, variances. comparison of two means and two proportions 1 2 1 2 ? ? p p μ μ = = comparison of two variances 9.1 ztests and confidence intervals for a difference between two population means Basic Assumptions: 1. 1 2 , , , m X X X L ~ rs from mean 1 μ and variance 2 1 σ 2. 1 2 , , , n Y Y Y L ~ rs from mean 2 μ and variance 2 2 σ 3. X and Y are independent of one another Prop) X Y ~ 2 2 1 2 1 2 ( , ) m n σ σ μ μ + 1 Case I : normal distribution with known variances X Y ~ 2 2 1 2 1 2 ( , ) N m n σ σ μ μ + 1 2 2 2 1 2 ( ) X Y m n μ μ σ σ + ~ ( 0, 1) N Test procedure: 1. Null Hypothesis: 1 2 : H μ μ = ∆ 2. test statistic: 2 2 1 2 X Y z m n σ σ ∆ = + 3. Alternative Hypothesis Rejection Region Pvalue 1 2 : a H μ μ ∆ z z α ≥ 1 ( ) z Φ 1 2 : a H μ μ < ∆ z z α ≤  ( ) z Φ 1 2 : a H μ μ ≠ ∆ / 2 z z α ≥ or / 2 z z α ≤  2[ 1 (   ) ] z Φ 2 Ex 9.1) Two different treatments (treatment vs control) the difference of two averages strengths of steels 29. 8, 20 34. 7, 25 x m y n = = = = 1. Parameter of interest: 1 2 μ μ =difference bet average strengths for the two types of steel 2. Null Hypothesis: 1 2 : H μ μ = 3. Alternative Hypothesis: 1 2 : a H μ μ ≠ 4. Test Statistic: 2 2 1 2 x y z m n σ σ = + 5. Rejection Region: 0. 005 2. 58 z z ≥ = or 0. 005 2. 58 z z ≤  =  6. Compute Statistic: 29. 8 34. 7 3. 66 16. 0 25. 0 20 25 z = =  + 7. Decide: 3.66<2.58, we reject the null hypothesis. The data strongly suggest that the two average strengths are different....
View
Full
Document
This note was uploaded on 01/06/2011 for the course STAT 511 taught by Professor Bud during the Fall '08 term at Purdue.
 Fall '08
 BUD
 Statistics, Variance

Click to edit the document details