Lecture #3 Learning Objectives1.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 Xis Normal and σis 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, σknown)Example 1: Revisiting Unlimited AvenueIn 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