This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Psych 100A Week 7 Discussion Notes Dawn Chen November 13, 2009 Confidence Intervals and Hypothesis Tests for the Difference between Two Independent Means 1 2 ( )  when 1 2 , are Known Conditions or Assumptions Goal Formula or Procedure Diagram of the Sampling Distribution of 1 2 x x Constructing a (1 ) 100%  confidence interval for 1 2  ( 29 1 2 1 2 2 x x x x z  If H is true: 1 2 : A H D  < 1 2 : A H D  1. 1 2 , are known 2. Scores for both populations are normally distributed or 1 2 , n n are large 3. Both samples are randomly chosen and independent from each other Conducting an independent samples ztest for 1 2  1. Formulate 1 2 : H D  = and 1 2 1 2 1 2 : , : , or : A A A H D H D H D  < 2. Calculate ( 29 1 2 1 2 obs x x x x D z  = 3. Reject H if: 1 2 1 2 2 1 2 if : ; if : ; if : obs A obs A obs A z z H D z z H D z z H D <  < 1 2 : A H D  Note: In the above table, 1 2 2 2 1 2 1 2 x x n n  = + is the standard deviation of the sampling distribution of 1 2 . x x (This formula comes from the fact that 2 2 2 X Y X Y  = + if X and Y are independent: 1 2 1 2 2 2 2 2 2 1 1 2 2 . x x x x n n  = + = + ) 2 2 D 1 2 x x  D 1 2 x x  D 1 2 x x  1  2 2 1 2  1 2 x x  Confidence Intervals and Hypothesis Tests for the Difference between Two Independent Means 1 2 ( )  when 1 2 , are Unknown but Equal Conditions or Assumptions Goal Formula or Procedure Diagram of the Sampling Distribution of 1 2 x x Constructing a (1 ) 100%  confidence interval for 1 2  ( 29 1 2 1 2 2, df x x x x t s  where 1 2 2 df n n = + If H is true: 1 2 : A H D  < 1 2 : A H D  1. 1 2 , are unknown, but 1 2 = 2. Scores for both populations are normally distributed or 1 2 , n n are large 3. Both samples are randomly chosen and independent from each other Conducting an independent samples ttest for 1 2  1. Formulate 1 2 : H D  = and 1 2 1 2 1 2 : , : , or : A A A H D H D H D  < 2. Calculate ( 29 1 2 1 2 obs x x x x D t s = 3. Reject H if: , 1 2 , 1 2 2, 1 2 if : ; if : ; if : obs df A obs df A obs df A t t H D t t H D t t H D <  < where 1 2 2 df n n = + 1 2 : A H D  Note: In the above table, 1 2 2 1 2 1 1 x x p s s n n = + where...
View
Full
Document
This note was uploaded on 09/24/2010 for the course STATS 13a taught by Professor Chen during the Spring '10 term at UCLA.
 Spring '10
 Chen
 Statistics

Click to edit the document details