10-1 Correlation 527 19. Oscars Listed below are ages of recent Oscar winners matched by the years in which the awards were won (from Data Set 21 “Oscar Winner Age” in Appendix B). Is there sufficient evidence to conclude that there is a linear correlation between the ages of Best Actresses and Best Actors? Should we expect that there would be a correlation? Best Actor 32 33 45 29 62 22 44 54 26 28 60 45 Best Actress 50 48 60 50 39 55 44 33 41 41 59 37 20. 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 linear 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 21. Prices of Pizza and Subway Rides The “pizza connection” is the principle that the price of a slice of pizza in New York City is always about the same as the subway fare. Use the pizza and subway cost data in the table below to determine whether there is a linear correlation between these two items. Year 1960 1973 1986 1995 2002 2003 2009 2013 2015 2019 Pizza Cost 0.15 0.35 1.00 1.25 1.75 2.00 2.25 2.30 2.75 3.00 Subway Fare 0.15 0.35 1.00 1.35 1.50 2.00 2.25 2.50 2.75 2.75 CPI 29.6 44.4 109.6 152.4 180.0 184.0 214.5 233.0 237.0 252.2 22. Subway and the CPI Use subway fare>CPI data from the preceding exercise to determine whether there is a significant linear correlation between the subway fare and the CPI (Consumer Price Index). 23. CSI Statistics Police crime scene investigators sometimes measure footprints at crime scenes so that they can learn something about criminals. Listed below are foot lengths (mm) and heights (mm) of males (from Data Set 3 “ANSUR II 2012” in Appendix B). Is there sufficient evidence to conclude that there is a linear correlation between foot lengths and heights of males? Based on these results, does it appear that police can use a footprint length to estimate the height of a male? Foot Length 282 278 253 259 279 258 274 262 Height 1785 1771 1676 1646 1859 1710 1789 1737 24. Crickets and Temperature A classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in °F (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 linear correlation 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 25. Car Sales and the Super Bowl Listed below are annual data for various years. The data are the numbers of cars sold (thousands) and the numbers of points scored in the Super Bowl. Is there sufficient evidence to conclude that there is a linear correlation between those two variables? Would it be reasonable to expect a correlation? Car Sales 8175 8213 8518 8991 8635 8527 8272 8142 Super Bowl Points 61 69 43 75 44 56 55 53
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