Theories have been developed about the heights of winning candidates for the U.S. presidency and the heights of candidates who were runners-up. Listed below are heights (in inches) from recent presidential elections. Is there a linear correlation between the heights of candidates who won and the heights of the candidates who were runners-up?

Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r from Table A-6 using ? = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables.

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Winner Runner-Up 72 69.5 73 69.5 73 70 74 68 74.5 74 74.5 74 71 73 71 76 TABLE A-6 Critical Values of the Pearson Correlation Coefficient r n TELEFONNING 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 α = .05 .950 .878 811 .754 .707 .666 .632 .602 576 .553 .532 .514 .497 482 468 .456 444 .396 .361 .335 312 294 279 254 236 220 207 .196 a = .01 .990 .959 .917 .875 .834 .798 .765 .735 .708 .684 .661 .641 .623 .606 .590 .575 .561 .505 .463 .430 .402 .378 .361 .330 .305 286 .269 .256