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Chapter_09

# Chapter_09 - Chinese 2202 Course Schedule Week 5 Week 6...

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Chapter 9: Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses Statistics

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McClave, Statistics, 11th ed. Chapter 9: Inferences Based on Two Samples 2 Where We’ve Been Made inferences based on confidence intervals and tests of hypotheses Studied confidence intervals and hypothesis tests for µ , p and 2 Selected the necessary sample size for a given margin of error
McClave, Statistics, 11th ed. Chapter 9: Inferences Based on Two Samples 3 Where We’re Going Learn to use confidence intervals and hypothesis tests to compare two populations Learn how to use these tools to compare two population means, proportions and variances Select the necessary sample size for a given margin of error when comparing parameters from two populations

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McClave, Statistics, 11th ed. Chapter 9: Inferences Based on Two Samples 4 9.1: Identifying the Target Parameter
McClave, Statistics, 11th ed. Chapter 9: Inferences Based on Two Samples 5 9.2: Comparing Two Population Means: Independent Sampling Point Estimators  → µ 1 -  2 µ 1 - µ 2 To construct a confidence interval or conduct a hypothesis test, we need the standard deviation: Singe sample n s x ˆ 2 2 2 1 2 1 2 1 ˆ n s n s x x Two samples

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McClave, Statistics, 11th ed. Chapter 9: Inferences Based on Two Samples 6 9.2: Comparing Two Population Means: Independent Sampling The Sampling Distribution for ( 1 - 2 ) 1. The mean of the sampling distribution is ( µ 1 - µ 2 ). 2. If the two samples are independent, the standard deviation of the sampling distribution (the standard error ) is 3. The sampling distribution for ( 1 - 2 ) is approximately normal for large samples. 2 2 2 1 2 1 2 1 ˆ n s n s x x
McClave, Statistics, 11th ed. Chapter 9: Inferences Based on Two Samples 7 9.2: Comparing Two Population Means: Independent Sampling The Sampling Distribution for ( 1 - 2 )

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McClave, Statistics, 11th ed. Chapter 9: Inferences Based on Two Samples 8 9.2: Comparing Two Population Means: Independent Sampling Large Sample Confidence Interval for ( µ 1 - µ 2 ) 2 2 2 1 2 1 2 / 2 1 2 2 2 1 2 1 2 / 2 1 ) ( 2 / 2 1 ) ( ) ( ) ( 2 1 n s n s z x x n n z x x z x x x x
9.2: Comparing Two Population Means: Independent Sampling Private Colleges n : 71 Mean: 78.17 Standard Deviation: 9.55 Variance: 91.17 Public Universities n : 32 Mean: 84 Standard Deviation: 9.88 Variance: 97.64 McClave, Statistics, 11th ed. Chapter 9: Inferences Based on Two Samples 9 Two samples concerning retention rates for first-year students at private and public institutions were obtained from the Department of Education’s data base to see if there was a significant difference in the two types of colleges.

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