600 CHAPTER 11 Goodness-of-Fit and Contingency Tables Statistical Literacy and Critical Thinking 1.Dogs Detecting Malaria The following table lists results from an experiment designed to test the ability of dogs to use their extraordinary sense of smell to detect malaria in samples of children’s socks (based on data presented at an annual meeting of the American Society of Tropical Medicine, by principal investigator Steve Lindsay). Assuming that the dog being correct is independent of whether malaria is present, find the expected value for the observed frequency of 123. Malaria Was Present Malaria Was Not Present Dog Was Correct 123 131 Dog Was Wrong 52 14 2.Identifying Hypotheses Refer to the data given in Exercise 1 and assume that the requirements are all satisfied and we want to conduct a hypothesis test of independence using the methods of this section. Identify the null and alternative hypotheses. 3.Hypothesis Test The accompanying TI-83>84 Plus calculator display shows the results from the experiment described in Exercise 1. Assume that the hypothesis test requirements are all satisfied. a. Identify the test statistic and the P-value (expressed in standard form and rounded to three decimal places), and then state the conclusion about the null hypothesis. b. Does rejection of the null hypothesis of independence imply that dogs are good at identifying malaria? 4.Right-Tailed, Left-Tailed, Two-Tailed Is the hypothesis test described in Exercise 1 righttailed, left-tailed, or two-tailed? Explain your choice. In Exercises 5–18, test the given claim. 5.Lie Detector The table below includes results from polygraph (lie detector) experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known if the subject lied or did not lie, so the table indicates when the polygraph test was correct. Use a 0.05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truths and lies? Did the Subject Actually Lie? No (Did Not Lie) Yes (Lied) Polygraph test indicated that the subject lied. 15 42 Polygraph test indicated that the subject did not lie. 32 9 6. Ghosts The following table summarizes results from a Pew Research Center survey in which subjects were asked whether they had seen or been in the presence of a ghost. Use a 0.01 significance level to test the claim that gender is independent of response. Does the conclusion change if the significance level is changed to 0.05? Yes No Male 138 724 Female 228 913 7.Texting and Drinking In a study of high school students at least 16 years of age, researchers obtained survey results summarized in the accompanying table (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” 11-2 Basic Skills and Concepts
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