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Lecture notes - inferences for two means (Part 1)

# Lecture notes - inferences for two means (Part 1) - Sec 9.2...

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Sec 9.2 Comparing two population means: independent sampling (large samples) 1. Independent samples Two samples are independent samples if the sample selected from one population has no effect on the sample selected from the other population. 2. Notation Population 1: µ 1 , σ 1 , n 1 , 1 x , s 1 Population 2: µ 2 , σ 2 , n 2 , 2 x , s 2 3. Case I Sampling distribution for 2 1 x x - (1) 2 1 2 1 μ μ μ - = - x x (2) 2 2 2 1 2 1 2 2 2 1 2 1 2 2 1 2 1 n n n n x x x x σ σ σ σ σ σ + = + = - - (3) If the sample sizes are large enough ( n 1 ≥30, n 2 ≥30), 2 1 x x - is approximately normally distributed. The standardized version of 2 1 x x - 2 2 2 1 2 1 2 1 2 1 2 2 2 1 2 1 2 1 2 1 ) ( ) ( n s n s x x n n x x z + - - - + - - - = μ μ σ σ μ μ has the standard normal distribution. 4. [Case I] Large-sample confidence interval for µ 1 - µ 2 ;and test of hypothesis conditions for Case I (1) indep samples (2) large samples (or normal populations, and known σ 1 and σ 2 ) (4a) The (1-α)100% confidence interval for µ 1 - µ 2 is 2 2 2 1 2 1 2 / 2 1 2 2 2 1 2 1 2 / 2 1 n s n s z x x n n z

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