CHAPTER 4 Cooperative Group Activities 201 FROM DATA TO DECISION Critical Thinking: Interpreting results from a test for smoking It is estimated that roughly half of smokers lie when asked about their smoking involvement. Pulse CO-oximeters may be a way to get information about smoking without relying on patients’ statements. Pulse CO-oximeters use light that shines through a fingernail, and it measures carbon monoxide in blood. These devices are used by firemen and emergency departments to detect carbon monoxide poisoning, but they can also be used to identify smokers. The accompanying table lists results from people aged 18–44 when the pulse CO-oximeter is set to detect a 6% or higher level of carboxyhemoglobin (based on data from “Carbon Monoxide Test Can Be Used to Identify Smoker,” by Patrice Wendling, Internal Medicine News, Vol. 40., No. 1, and Centers for Disease Control and Prevention). CO-Oximetry Test for Smoking Positive Test Result Negative Test Result Smoker 49 57 Nonsmoker 24 370 Analyzing the Results 1. False Positive Based on the results in the table, find the probability that a subject is not a smoker, given that the test result is positive. 2. True Positive Based on the results in the table, find the probability that a subject smokes, given that the test result is positive. 3. False Negative Based on the results in the table, find the probability that a subject smokes, given that the test result is negative. 4. True Negative Based on the results in the table, find the probability that a subject does not smoke, given that the test result is negative. 5. Sensitivity Find the sensitivity of the test by finding the probability of a true positive, given that the subject actually smokes. 6. Specificity Find the specificity of the test by finding the probability of a true negative, given that the subject does not smoke. 7. Positive Predictive Value Find the positive predictive value of the test by finding the probability that the subject smokes, given that the test yields a positive result. 8. Negative Predictive Value Find the negative predictive value of the test by finding the probability that the subject does not smoke, given that the test yields a negative result. 9. Confusion of the Inverse Find the following values, then compare them. In this case, what is confusion of the inverse? • P(smoker positive test result) • P(positive test result smoker) 10. Effectiveness of the Test Based on the results found, what do you conclude about the effectiveness of pulse CO-oximeters used to identify smokers? Cooperative Group Activities 1.Out-of-class activity Divide into groups of three or four and create a new carnival game. Determine the probability of winning. Determine how much money the operator of the game can expect to gain each time the game is played. 2. In-class activity Divide into groups of three or four and use coin flipping to develop a simulation that emulates the kingdom that abides by this decree: After a mother gives birth to a son, she will not have any other children. If this decree is followed, does the proportion of girls increase? 3.In-class activity Divide into groups of three or four and use actual thumbtacks or Hershey’s Kisses candies or paper cups to estimate the probability that when dropped, they will land with the point (or open side) up. How many trials are necessary to get a result that appears to be reasonably accurate when rounded to the first decimal place?
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