sLecture3cPBS - Lecture #3 Learning Objectives 1. Learn how...

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Lecture #3 Learning Objectives 1. Learn how to formulate hypotheses about a population mean. 2. Know how to conduct a test of significance about a population mean when the sampling distribution of X is Normal and σ is known a. Using a P -value. b. Using the “significance region” or “critical value” method. c. Using a confidence interval estimate. 3. Be able to state appropriate conclusions about the population mean and the specific business problem based on the results of an hypothesis test. 4. Know the errors that can be made when conducting an hypothesis test. 5. Know the definition of the following terms: Null Hypothesis Alternative Hypothesis Critical Value Level of Significance Two-Tail Test Type I Error One-Tail Test Type II Error p -value “I have no special talent. I am only passionately curious.” - Albert Einstein (1879 – 1955)
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BM330 - Lecture 3 Hypothesis Tests About the Population Mean (Independent sample observations, X ~Normal, σ known) Example 1 : Revisiting Unlimited Avenue In Lectures 1 and 2, we discussed the proposed chain of up-scale stores designed to market high-end woman’s fashions called Unlimited Avenue . We need to evaluate the annual household income in a given market location. It has been stated that the average household income needed to make the store location successful must exceed $50,000 per year. Recall that the market research staff at the Limited collected a random sample of 64 households from the geographical area in question and found an average annual income of $50,725. We assumed that the standard deviation for household incomes is $4,200. At issue is which of the two following possibilities is more likely: 1. μ $50,000, i.e., the mean annual income does not exceed $50,000 2. μ > $50,000, i.e., the mean annual income exceeds $50,000 1
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The Hypotheses In hypothesis testing the two possibilities outlined above would be formally stated as the hypotheses. The first statement is called the null hypothesis , and is denoted by H 0 (read H zero). The second statement is called the alternative hypothesis and is denoted by H a (read H a). This is sometimes called the research hypothesis, and may be denoted H A or H 1 . The parameter value specified in H 0 is called the null value. H 0 : μ $50,000 = μ 0 H a : μ > $50,000 Note that one of these two statements must be true. Testing Significance On the basis of sample information, we will determine which of the two hypotheses is more reasonable. Is our sample outcome ( x = $50,725) extreme enough to support that the alternative hypothesis is true, i.e., we believe μ > $50,000? If so, we “reject” H 0 , and we say that the sample result is _________________ . Or, is our sample outcome close enough to $50,000 that we “cannot reject” the null hypothesis? In this case, the amount that X is above $50,000 could be attributed to sampling error. If so, we say that the sample result is _____________________________. 2
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This note was uploaded on 02/22/2009 for the course BUSMGT 330m taught by Professor Kriska during the Spring '08 term at Ohio State.

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sLecture3cPBS - Lecture #3 Learning Objectives 1. Learn how...

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