two sample test

# two sample test - Inference on two population means and...

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Inference on two population means and proportions Inferences About the Difference Between Two Population Means: s 1 and 2 Known Inferences About the Difference Between Two Population Proportions Inferences About the Difference Between Two Population Means: Matched Samples Inferences About the Difference Between Two Population Means: 1 and 2 Unknown

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Estimating the Difference Between Two Population Means Let 1 equal the mean of population 1 and 2 equal the mean of population 2. The difference between the two population means is 1 - 2 . Let equal the mean of sample 1 and equal the mean of sample 2. The point estimator of the difference between the means of the populations 1 and 2 is . 1 x 2 x 2 1 x x
Expected Value Sampling Distribution of Standard Deviation (Standard Error) where: s 1 = standard deviation of population 1 2 = standard deviation of population 2 n 1 = sample size from population 1 n 2 = sample size from population 2 2 2 2 1 2 1 2 1 n n x x 2 1 2 1 ) (  x x E 2 1 x x

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Interval Estimate Interval Estimation of 1 - 2 : s 1 and 2 Known 2 2 2 1 2 1 2 / 2 1 n n z x x Example In a test of driving distance using a mechanical driving device, a sample of Par golf balls was compared with a sample of golf balls made by Rap, Ltd., a competitor. The sample statistics appear on the next slide.
Example: Par, Inc. Interval Estimation of 1 - 2 : s 1 and 2 Known Sample Size Sample Mean Sample #1 Par, Inc. Sample #2 Rap, Ltd. 120 balls 80 balls 275 yards 258 yards Based on data from previous driving distance tests, the two population standard deviations are known with 1 = 15 yards and 2 = 20 yards.

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Interval Estimation of 1 - 2 : s 1 and 2 Known Example: Par, Inc. Let us develop a 95% confidence interval estimate of the difference between the mean driving distances of the two brands of golf ball. 80 ) 20 ( 120 ) 15 ( 96 . 1 17 2 2 2 2 2 1 2 1 2 / 2 1 n n z x x We are 95% confident that the difference between the mean driving distances of Par, Inc. balls and Rap, Ltd. balls is 11.86 to 22.14 yards. 17 + 5.14 or 11.86 yards to 22.14 yards
Hypothesis Tests About 1   2 : s 1 and 2 Known Hypotheses 1 2 0 22 12 () x x D z nn ss    1 2 0 : a HD  0 1 2 0 :  0 1 2 0 :  1 2 0 : a  0 1 2 0 :  1 2 0 : a Left-tailed Right-tailed Two-tailed Test Statistic

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Example: Par, Inc. Hypothesis Tests About 1   2 : s 1 and 2 Known Can we conclude, using = .01, that the mean driving distance of Par, Inc. golf balls is greater than the mean driving distance of Rap, Ltd. golf balls?
H 0 : 1 - 2 < 0 H a : 1 - 2 > 0 where: 1 = mean distance for the population of Par, Inc. golf balls 2 = mean distance for the population of Rap, Ltd. golf balls 1. Develop the hypotheses.

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## This note was uploaded on 09/28/2011 for the course STAT METHO 33:623:385 taught by Professor Faridalizadeh during the Spring '11 term at Rutgers.

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two sample test - Inference on two population means and...

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