Chapter16_STAT1100_LC.ppt", filename="Chapter16_STAT1100_LC.ppt", filename="Chap

Chapter16_STAT1100_LC.ppt", filename="Chapter16_STAT1100_LC.ppt", filename="Chap

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χ 2 (Chi-Squared) Tests Statistics for Management and Economics Chapter 16
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A Common Theme What to do? Data Type? Number of  Categories? Statistical  Technique: Describe a  population Nominal Two or more χ 2  goodness of  fit test Compare two  populations Nominal χ 2  test of a  contingency  table Compare two or  more populations Nominal χ 2  test of a  contingency  table Analyze  relationship  between two  variables Nominal χ 2  test of a  contingency  table One data type… …Two techniques
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Two Techniques The first is a goodness-of-fit test applied to data produced by a multinomial experiment , a generalization of a binomial experiment and is used to describe one population of data. The second uses data arranged in a contingency table to determine whether two classifications of a population of nominal data are statistically independent ; this test can also be interpreted as a comparison of two or more populations. In both cases, we use the chi-squared ( χ 2 ) distribution.
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The Multinomial Experiment Unlike a binomial experiment which only has two possible outcomes (e.g. heads or tails), a multinomial experiment : Consists of a fixed number, n , of trials. Each trial can have one of k outcomes, called cells. Each probability p i remains constant. Our usual notion of probabilities holds, namely: p 1 + p 2 + … + p k = 1, and Each trial is independent of the other trials.
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χ 2 Goodness-of-Fit Test How can the chi-square goodness of fit (GOF) test be applied to business situations? One survey of U.S. consumers conducted by the Wall Street Journal and NBC News asked the question: “In general, how would you rate the level of service that American businesses provide?” The distribution of responses to this question was as follows: 8% Excellent, 47% Pretty good, 34% Only fair, and 11% Poor. Suppose a store manager wants to find out whether the results of this consumer survey apply to customers of supermarkets in her city. To do so, she interviews 207 randomly selected consumers as they leave supermarkets in various parts of the city. She asks the customers how they would rate the level of service at the supermarket from which they had just exited. The response categories are excellent, pretty good, only fair, and poor. The observed responses are used to calculate the proportion in this sample within each of those categories.
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This note was uploaded on 06/25/2008 for the course BUSSPP MCE taught by Professor Atkins during the Spring '08 term at Pittsburgh.

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Chapter16_STAT1100_LC.ppt", filename="Chapter16_STAT1100_LC.ppt", filename="Chap

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