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M316 Chapter 23

Itiszeroexactlywhenthereareno 5 m316 chapter23 drberg

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Unformatted text preview: f a binomial random variable np. For example, the proportion of subjects in the study who experienced a much better quality of life is count of successes row 1 total 661 . p= = = table total table total 2476 616 Thus np = ( 311) = 77.37 . 2476 € Exercise (23.6) Attitudes Toward Recycled Products The null hypothesis in Exercise 23.2 says that in the population of all € consumers, the proportions of people who hold each attitude are the same for buyers and non‐buyers. a) Find the expected cell counts if this hypothesis is true and display them in a two‐way table. b) Are there any large deviations between the observed counts and the expected counts? What kind of relationship is indicated? The Chi‐Square Test The statistical test that tells us whether the observed differences are statistically significant is the chi‐square test. The Chi‐Square Statistic The chi­square statistic is a measure of how far the observed counts in a two‐way table are from the expected counts. The formula is (observed count – expected count)2 Χ2 = ∑ . expected count The sum is over all cells in the table. We think of the chi‐square statistic as a measure of distance, and like any € measure of distance, it is never negative. It is zero exactly when there are no 5 M316 Chapter 23 Dr. Berg differences between the expected counts and the observed counts. This is a rare occurrence because of random variation. Large values of Χ2 are evidence against H0. Although the alternative hypothesis is many sided, the chi‐square test is one‐sided because any...
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