484 CHAPTER 9 Correlation and Regression The t-Test for Correlation Coefficients In Exercises 33–36, perform a hypothesis test using Table 5 in Appendix B to make a conclusion about the correlation coefficient. 33. Braking Distances: Dry Surface The weights (in pounds) of eight vehicles and the variabilities of their braking distances (in feet) when stopping on a dry surface are shown in the table. At a = 0.01, is there enough evidence to conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a dry surface? (Adapted from National Highway Traffic Safety Administration) Weight, x 5940 5340 6500 5100 5850 4800 5600 5890 Variability, y 1.78 1.93 1.91 1.59 1.66 1.50 1.61 1.70 34. Braking Distances: Wet Surface The weights (in pounds) of eight vehicles and the variabilities of their braking distances (in feet) when stopping on a wet surface are shown in the table. At a = 0.05, is there enough evidence to conclude that there is a significant linear correlation between vehicle weight and variability in braking distance on a wet surface? (Adapted from National Highway Traffic Safety Administration) Weight, x 5890 5340 6500 4800 5940 5600 5100 5850 Variability, y 2.92 2.40 4.09 1.72 2.88 2.53 2.32 2.78 35. Maximal Strength and Jump Height The table in Exercise 25 shows the maximum weights (in kilograms) for which one repetition of a half squat can be performed and the jump heights (in centimeters) for 12 international soccer players. At a = 0.05, is there enough evidence to conclude that there is a significant linear correlation between the data? (Use the value of r found in Exercise 25.) 36. Maximal Strength and Sprint Performance The table in Exercise 26 shows the maximum weights (in kilograms) for which one repetition of a half squat can be performed and the times (in seconds) to run a 10-meter sprint for 12 international soccer players. At a = 0.01, is there enough evidence to conclude that there is a significant linear correlation between the data? (Use the value of r found in Exercise 26.) Extending Concepts 37. Interchanging x and y In Exercise 26, let the time (in seconds) to sprint 10 meters represent the x@values and the maximum weight (in kilograms) for which one repetition of a half squat can be performed represent the y@values. Calculate the correlation coefficient r. What effect does switching the explanatory and response variables have on the correlation coefficient? 38. Writing Use an appropriate research source to find a real-life data set with the indicated cause-and-effect relationship. Write a paragraph describing each variable and explain why you think the variables have the indicated cause-and-effect relationship. (a) Direct Cause-and-Effect: Changes in one variable cause changes in the other variable. (b) Other Factors: The relationship between the variables is caused by a third variable. (c) Coincidence: The relationship between the variables is a coincidence.
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