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Unformatted text preview: Chapter 10 Statistical Inference about Means and Proportions with Two Populations Outline: • Estimation of the difference between means of two populations: 1. Point estimator of the difference between the means of the populations. 2. Sampling distribution of the point estimator. 3. Interval estimate of μ 1μ 2 : Large Sample Case. 4. Interval estimate of μ 1μ 2 : Small Sample Case. • Hypothesis tests about the difference between the means of two populations: Independent Samples. • Inferences about the difference of means: Matched Samples. Point Estimator for μ 1μ 2 1. Select a simple random sample of size n 1 from population 1 and compute 1 x . 2. Select a simple random sample of size n 2 from population 2 and compute 2 x . 3. Compute the point estimator: 2 1 x x . 1 Sampling Distribution of 2 1 X X : Expected Value of 2 1 X X : The point estimator of the difference of means ( 2 1 μ μ  ) is 2 1 X X Standard Deviation of 2 1 X X : (Aside) An easier way to remember is that where σ 1 = standard deviation of population 1 σ 2 = standard deviation of population 2 n 1 = sample size from population 1 n 2 = sample size from population 2 2 2 1 2 1 ) ( μ μ = X X E 2 2 2 1 2 1 2 1 n n X X σ + σ = σ 2 2 2 2 1 2 1 X X X X σ + σ = σ Interval Estimate of μ 1μ 2 : Large Sample (n 1 > 30 and n 2 > 30) • σ 1 known and σ 2 known where 1 α is the confidence coefficient • σ 1 unknown and σ 2 unknown where 3 2 1 2 / 2 1 ) ( X X z x x α σ ± 2 1 2 / 2 1 ) ( X X s z x x α ± 2 2 2 1 2 1 2 1 n s n s s X X + = Example: Par, Inc. Par, Inc. is a manufacturer of golf equipment and has developed a new golf ball to provide extra distance . In a test of the driving distance using a mechanical device, a sample of golf balls was compared with a sample of golf balls from a competitor (Rap, Ltd.) • Sample Statistics Sample #1 Sample #2 Par, Inc. Rap, Ltd . Sample Size n 1 = 120 balls n 2 = 80 balls Mean 1 x = 235 yards 2 x = 218 yards Standard Dev. s 1 = 15 yards s 2 = 20 yards • Point Estimate of the difference between the populations, where μ 1 is the mean driving distance of golf balls from Par, Inc.; μ 2 is the mean driving distance of golf balls from Rap, Ltd....
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This note was uploaded on 01/31/2011 for the course MGMT 305 taught by Professor Priya during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Priya

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