526 CHAPTER 10 Correlation and Regression Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.) 13. Powerball Jackpots and Tickets Sold Listed below are the same data from Table 10-1 in the Chapter Problem, but an additional pair of values has been added in the last column. Is there sufficient evidence to conclude that there is a linear correlation between lottery jackpot amounts and numbers of tickets sold? Comment on the effect of the added pair of values in the last column. Compare the results to those obtained in Example 4 on pages 515 and 516. Jackpot 334 127 300 227 202 180 164 145 255 400 Tickets 54 16 41 27 23 18 18 16 26 17 14. Powerball Jackpots and Tickets Sold Listed below are the same data from Table 10-1 in the Chapter Problem, but an additional pair of values has been added from actual Powerball results. Is there sufficient evidence to conclude that there is a linear correlation between lottery jackpots and numbers of tickets sold? Comment on the effect of the added pair of values in the last column. Compare the results to those obtained in Example 4. Jackpot 334 127 300 227 202 180 164 145 255 625 Tickets 54 16 41 27 23 18 18 16 26 90 15. Taxis The table below includes data from New York City taxi rides (from Data Set 32 “Taxis” in Appendix B). The distances are in miles, the times are in minutes, the fares are in dollars, and the tips are in dollars. Is there sufficient evidence to support the claim that there is a linear correlation between the time of the ride and the tip amount? Does it appear that riders base their tips on the time of the ride? Distance 0.68 2.47 8.5112.71 1.651.02 1.32 0.49 Time 6.00 18.00 31.00 27.00 11.00 8.00 8.00 2.00 Fare 6.3014.3031.7536.80 9.807.80 7.80 4.80 Tip 1.89 4.29 2.98 0.00 1.962.34 0.00 0.00 16. Taxis Using the data from Exercise 15, is there sufficient evidence to support the claim that there is a linear 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? 17. Taxis Using the data from Exercise 15, is there sufficient evidence to support the claim that there is a linear correlation between the distance of the ride and the fare (cost of the ride)? 18. Taxis Using the data from Exercise 15, is there sufficient evidence to support the claim that there is a linear correlation between the time of the ride and the fare (cost of the ride)? Explore! Exercises 11 and 12 provide two data sets from “Graphs in Statistical Analysis,” by F. J. Anscombe, the American Statistician, Vol. 27. For each exercise, a. Construct a scatterplot. b. Find the value of the linear correlation coefficient r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. 11. x 10 8 13 9 11 14 6 4 12 7 5 y 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74 12. x 10 8 13 9 11 14 6 4 12 7 5 y 7.46 6.77 12.74 7.11 7.81 8.84 6.08 5.39 8.15 6.42 5.73
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