Week7_Notes

Week7_Notes - Psych 100A Week 7 Discussion Notes Dawn Chen...

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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 z-test 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 t-test 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...
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This note was uploaded on 09/24/2010 for the course STATS 13a taught by Professor Chen during the Spring '10 term at UCLA.

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Week7_Notes - Psych 100A Week 7 Discussion Notes Dawn Chen...

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