MQM100_HypothesisTest_OnePopulation

MQM100_HypothesisTest_OnePopulation - MQM-100 Chapter 7:...

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1 MQM-100 Chapter 7: Sampling Distributions ( x , p ˆ , ( 1 x - 2 x ), ( 1 ˆ p - 2 ˆ p ) ) Chapter 8: Estimation of µ & P and determine sample size (n) -- One Population Chapter 9: Hypothesis Tests of µ & P -- One Population Chapter 10: Estimation & Hypothesis Tests of Means & Proportions -- Two Population Chapter 9: Hypothesis Tests about the Mean ( µ ) and Proportion (P)-- One Population 1. Concepts of Hypothesis Test 2. Components (3) of Hypothesis Testing: B) Test Statistic, or P-value, or Confidence Interval. C) Conclusion/Decision. 3. Hypothesis Test about a PARAMETER: e.g., µ , P 4. Hypothesis Test about a population mean ( µ ): i) σ 2 - Known, ii) σ 2 - Unknown but n 30, iii) σ 2 - Unknown but n < 30 5. Example of hypothesis test about a population mean: using three (3) different approach. 6. Hypothesis Test about a population proportion (P).
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2 Testing Hypothesis About Population Parameters (pp.377-378) Toothpaste Example: Marketing a new brand-A tooth paste. Hypothesis No. 1 : More than 50% of all consumers prefer brand A. Sample of 100: 99 prefer brand A Conclusion: hypothesis is true. Hypothesis No. 2 : Less than 50% of all consumers prefer brand A. Sample of 100: 99 prefer brand A (a rare event and the probability is small). Conclusion: hypothesis is not true. The Null Hypothesis is the hypothesis being tested and is denoted by H 0 . (p-378) The Alternative Hypothesis is the opposite of the H 0 and describes the desired goal of the experiment denoted by H a (or H 1 ) which is our research hypothesis. (p-378) A test statistic is a statistic which is used in the testing of H 0 , e.g. Z, t, F, etc. Since a test statistic is a random variable, it has a probability distribution. Type I Error and Type II Error. (p-380) Level of significance (or significance level) is denoted by α . Probability (type I error) = α Probability (type II error) = β Probability (reject H 0 /H 0 False) = 1 - β Power of the test = 1 - β Type I and Type II Errors (p-381) H 0 is true H 0 is false Do not Correct decision Type II error Reject H 0 Prob. is 1- α P (Type II error) = β Reject H 0 Type I error Correct decision P (Type I error) = α Prob. is 1- β
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3 Components of Hypothesis Testing 1. Null hypothesis: specifies a value of the parameter. Example: H
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MQM100_HypothesisTest_OnePopulation - MQM-100 Chapter 7:...

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