590 CHAPTER 11 Goodness-of-Fit and Contingency Tables 24. Author’s Computer Files The author recorded the leading digits of the sizes of the electronic document files for the current edition of this book. The leading digits have frequencies of 112, 28, 62, 47, 32, 40, 24, 11, and 11 (corresponding to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively). Using a 0.05 significance level, test for goodness-of-fit with Benford’s law. 25. Testing Goodness-of-Fit with a Normal Distribution Refer to Data Set 1 “Body Data” in Appendix B for the heights of females. Height (cm) Less than 155.45 155.45 − 162.05 162.05 − 168.65 Greater than 168.65 Frequency a. Enter the observed frequencies in the table above. b. Assuming a normal distribution with mean and standard deviation given by the sample mean and standard deviation, use the methods of Chapter 6 to find the probability of a randomly selected height belonging to each class. c. Using the probabilities found in part (b), find the expected frequency for each category. d. Use a 0.01 significance level to test the claim that the heights were randomly selected from a normally distributed population. Does the goodness-of-fit test suggest that the data are from a normally distributed population? 26.Weights Measured or Reported? Use the last digits of reported weights (lb) of females from Data Set 4 “Measured and Reported” and test to determine whether they occur with about the same frequency. Use a 0.05 significance level. How do the results confirm that the weights were reported and not measured? Also, what is it about the measured weights (lb) of females that strongly suggests that they were in fact measured and not reported? 11-1 Beyond the Basics Key Concept We now consider methods for analyzing contingency tables (or twoway frequency tables), which include frequency counts for categorical data arranged in a table with at least two rows and at least two columns. In Part 1 of this section, we present a method for conducting a hypothesis test of the null hypothesis that the row and column variables are independent of each other. This test of independence is widely used in real-world applications. In Part 2, we will consider three variations of the basic method presented in Part 1: (1) test of homogeneity, (2) Fisher’s exact test, and (3) McNemar’s test for matched pairs. 11-2 Contingency Tables PART 1 Basic Concepts of Testing for Independence In this section we use standard statistical methods to analyze frequency counts in a contingency table (or two-way frequency table). DEFINITION A contingency table (or two-way frequency table) is a table consisting of frequency counts of categorical data corresponding to two different variables. (One variable is used to categorize rows, and a second variable is used to categorize columns.)
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