REAL STATISTICS REAL DECISIONS Putting it all together 578 CHAPTER 10 Chi-Square Tests and the F-Distribution Fraud.org was created by the National Consumers League (NCL) to combat the growing problem of telemarketing and Internet fraud by improving prevention and enforcement. NCL works to protect and promote social and economic justice for consumers and workers in the United States and abroad. You work for the NCL as a statistical analyst. You are studying data on fraud. Part of your analysis involves testing the goodness-of-fit, testing for independence, comparing variances, and performing ANOVA. EXERCISES 1. Goodness-of-Fit The table at the right shows an expected distribution of the ages of fraud victims. The table also shows the results of a survey of 1000 randomly selected fraud victims. Using a = 0.01, perform a chi-square goodness-of-fit test. What can you conclude? 2. Independence The contingency table below shows the results of a random sample of 2000 fraud victims classified by age and type of fraud. The frauds were committed using bogus sweepstakes or credit card offers. (a) Calculate the expected frequency for each cell in the contingency table. Assume the variables age and type of fraud are independent. (b) Can you conclude that the ages of the victims are related to the type of fraud? Use a = 0.01. Type of Fraud Age Under 20 20–29 30–39 40–49 50–59 60–69 70–79 80+ Total Sweepstakes 10 60 70 130 90 160 280 200 1000 Credit cards 20 180 260 240 180 70 30 20 1000 Total 30 240 330 370 270 230 310 220 2000 Age Expected distribution Survey results Under 18 0.71% 8 18–25 13.39% 148 26–35 15.54% 166 36–45 16.38% 185 46–55 14.00% 131 56–65 15.94% 153 Over 65 24.05% 209 TABLE FOR EXERCISE 1
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