1. **State the problem:** We need to create a two-way table summarizing the drug test results of marathon runners based on whether they finished in the top 10 or not, and whether they tested positive or negative. 2. **Given data:** - Total runners who tested positive: 23 - Of those positive, 6 finished in the top 10 - Total runners who tested negative: 35 3. **Calculate the number of positive testers not in top 10:** $$23 - 6 = 17$$ 4. **Calculate the total number of runners:** $$23 + 35 = 58$$ 5. **Calculate the number of runners in top 10 who tested negative:** We know 6 positive tested runners are in top 10, but total top 10 runners is unknown. However, since the problem only asks for the table, we can find the negative testers in top 10 by subtracting positive top 10 from total top 10. 6. **Calculate the number of runners not in top 10 who tested negative:** Since total negative testers are 35, and some are in top 10, the rest are not in top 10. 7. **Find the number of negative testers in top 10:** Total top 10 runners = positive top 10 + negative top 10 We don't have total top 10 runners, but we can find negative top 10 by subtracting positive top 10 from total top 10. Since the problem only provides data for positive testers in top 10 and total negative testers, we assume the rest of the negative testers are not in top 10. 8. **Calculate negative testers not in top 10:** Since no data on negative testers in top 10, assume all 35 negative testers are not in top 10. 9. **Fill the table:** | | Top 10 | Not top 10 | |-----------------|--------|------------| | Positive test | 6 | 17 | | Negative test | 0 | 35 | **Final two-way table:** Top 10 | Not top 10 Positive test | 6 | 17 Negative test | 0 | 35