Exam 12: The Analysis of Categorical Data and Goodness-Of-Fit Tests

Suppose that we are studying the purchasing behavior of individuals buying breakfast oatmeal. We hypothesize that half the cereal purchases will be the big name brand, "Seabiscuit Oats" and that the remaining purchases will be divided equally between two local brands, "Secretariat Oats" and "Whirlaway Oats." a) Define appropriate statistical variables, and use them to state the null and alternative hypothesis that would be used to decide if there was convincing evidence against the hypothesized distribution of purchases across the three brands. b) Suppose that each individual in a random sample of 200 purchasers provides information about his or her choice of brand. For each category, what are the expected values? c) How many degrees of freedom are associated with the chi-squared goodness-of-fit statistic? d) Suppose that χ² = 6.10. What can be said about the P-value for this hypothesis test?

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