13-6 Rank Correlation 685 The purpose of the study was to determine if weights of seals could be determined from overhead photographs. Is there sufficient evidence to conclude that there is a correlation between overhead widths and the weights of the seals? Overhead width (cm) 7.2 7.4 9.8 9.4 8.8 8.4 Weight (kg) 116 154 245 202 200 191 10. Cheese and Engineering Listed below are annual data for various years. The data are weights (pounds) of per capita consumption of mozzarella cheese and the numbers of civil engineering PhD degrees awarded (based on data from the U.S. Department of Agriculture and the National Science Foundation). Is there sufficient evidence to conclude that there is a correlation between the two variables? What important comment should be made about the conclusion? Cheese Consumption 9.3 9.7 9.7 9.7 9.9 10.2 10.5 11.0 10.6 10.6 Civil Engineering PhDs 480 501 540 552 547 622 655 701 712 708 11. POTUS Media periodically discuss the issue of heights of winning presidential candidates and heights of their main opponents. Listed below are those heights (cm) from several recent presidential elections (from Data Set 22 “Presidents” in Appendix B). Is there sufficient evidence to conclude that there is a correlation between heights of winning presidential candidates and heights of their main opponents? Should there be such a correlation? President 192 182 177 185 188 188 183 188 191 Opponent 180 180 183 177 173 188 185 175 169 12. Crickets and Temperature The association between the temperature and the number of times a cricket chirps in 1 min was studied. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in degrees Fahrenheit (based on data from The Song of Insects by George W. Pierce, Harvard University Press). Is there sufficient evidence to conclude that there is a relationship between the number of chirps in 1 min and the temperature? Chirps in 1 min 882 1188 1104 864 1200 1032 960 900 Temperature 1°F2 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6 Appendix B Data Sets. In Exercises 13–16, use the data in Appendix B to test for rank correlation with a 0.05 significance level. 13. Taxis Refer to Data Set 32 “Taxis” in Appendix B and use the distances (miles) and tip amounts (dollars) of all of the rides. Is there sufficient evidence to support the claim that there is a correlation between the distance of the ride and the tip amount? Does it appear that riders base their tips on the distance of the ride? 14. Taxis Refer to Data Set 32 “Taxis” in Appendix B and use the distances (miles) and the times (minutes) of all of the rides. Is there sufficient evidence to support the claim that there is a correlation between the distance of the ride and the time of the ride? 15. Ages of Best Actresses and Best Actors Use the ages of Best Actresses and Best Actors at the times they won Oscars (from Data Set 21 “Oscar Winner Age” in Appendix B). Do these data suggest that there is a correlation between ages of Best Actresses and Best Actors? 16. IQ and Brain Volume Refer to Data Set 12 “IQ and Brain Size” in Appendix B and test for a correlation between brain volume (cm3) and IQ score.
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