Example 5: Accuracy of Lie Detectors Tonight Participants in a study to evaluate the accuracy of lie detectors were divided into two groups, with one group reading true material and the other group reading false material, while connected to a lie detector. Both groups received electric shocks to add stress. The two way table indicates whether the participants were lying or telling the truth and also whether the lie detector indicated they were lying or not. a. Are the conditions met for using the normal distribution? Detector Detector b. Find the three sample proportions for the proportion of says lying says not Total 31 17 48 times the lie detector says the person is lying (the Person lying proportion for the lying people, the proportion for the Person not lying 27 21 48 truthful people, and the pooled proportion) Total 58 38 96 c. Test to see if there is a difference in the proportion of times the lie detector says the person is lying, depending on whether the person is lying or telling the truth. Show all details of the test. Example 6: Tagging Penguins A study was conducted to see if tagging penguins with metal tags harms them. In the study, 100 penguins were randomly assigned to receive a metal tag or (as a control group) an electronic tag. One of the variables studied is survival rate ten years after the penguins were tagged. The scientists observed that 10 of the 50 metal tagged penquins survived while 18 of the 50 electronic penguins survived. a. Create a two-way table of the data. Include row and column totals. b. Are the conditions met for using the normal distribution? C. Test to see if the survival rate is lower for metal-tagged penguins than for electronic-tagged penguins. Do metal tags appear to reduce survival rate in penguins? The