BUS152-Ch09 - Chapter 9 Fundamentals of Hypothesis Testing:...

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1 Chapter 9 – Fundamentals of Hypothesis Testing: One-Sample Tests n A hypothesis is a claim (assumption) about a population parameter (not about a sample statistic): n population mean e.g., The mean monthly cell phone bill in this city is μ = $42 n population proportion e.g., The proportion of adults in this city with cell phones is π = 0.68 Null and Alternative Hypotheses Null Hypothesis, H 0 States the claim or assertion to be tested e.g., The population mean age is 50 ± : ² = 50 Begin with the assumption that the null hypothesis is true Always contains “=” , “ ” or “ ” sign Alternative Hypothesis, H 1 Is the opposite of the null hypothesis e.g. The population mean age is not 50 ³ : ² ≠ 50 Never contains the “=” , “ ” or “ ” sign § If you reject the null hypothesis, you have statistical proof that the alternative hypothesis is correct. § If you do not reject the null hypothesis, have failed to prove the alternative hypothesis. The failure prove the alternative hypothesis, however, does not mean that you have proven the null hypothesis. Hypothesis Testing Process n Claim: The population mean age is 50. n H 0 : μ = 50, H 1 : μ 50 Sample the population and find sample mean. Suppose the sample mean age was ´ µ = 20. Is the sample mean close the assumed population mean? If close, the null hypothesis is not rejected. If far, the null hypothesis is rejected. How far is “far enough” to reject H 0 ? Two ways of understanding “far enough”: 1. Test Statistic and Critical Value 2. p -Value
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2 Risks in Decision Making: Actual Situation Decision H 0 True H 0 False Do not reject H 0 Correct decision Confidence = (1 ) Type II error Probability = ± Reject H 0 Type I error Probability = Correct decision Power = (1 − ± ) n The confidence coefficient (1- α ) is the probability of not rejecting H 0 when it is true.
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This note was uploaded on 12/22/2011 for the course BUSINESS bus 152 taught by Professor Çeşmecibaşı during the Spring '11 term at Middle East Technical University.

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BUS152-Ch09 - Chapter 9 Fundamentals of Hypothesis Testing:...

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