80 CHAPTER 2 Exploring Data with Tables and Graphs 3. Scatterplot What is a scatterplot and how does it help us? 4. Estimating r For each of the following, estimate the value of the linear correlation coefficient r for the given paired data obtained from 50 randomly selected adults. a. Their heights are measured in inches 1x2 and those same heights are recorded in centimeters 1y2. b. Their IQ scores 1x2 are measured and their heights 1y2 are measured in centimeters. c. Their pulse rates 1x2 are measured and their IQ scores are measured 1y2. d. The 50 adults all drove cars from Jacksonville, Florida, to Richmond, Virginia. Their average (mean) speeds 1x2 are recorded along with the times 1y2 it took to complete that trip. Scatterplot. In Exercises 5–8, use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation? 5. Forecast and Actual Temperatures The table lists actual high temperatures and the high temperatures that were previously forecasted for these same days. The table includes data for ten different days near the author’s home. What does the result suggest about the accuracy of five-day predicted high temperatures? Actual High 80 77 81 85 73 73 80 72 83 81 Predicted High 56 57 59 56 64 57 61 63 59 61 6. Airport Data Speeds Listed below are the cellular data speeds (Mbps) from Sprint and Verizon measured at nine different airports (based on data from CNN). What would the presence of a correlation suggest about Sprint and Verizon? Sprint 13.0 30.4 15.2 2.4 2.7 2.1 0.8 1.6 5.6 Verizon 38.5 55.6 22.4 14.1 23.1 24.5 6.5 21.5 25.7 7. Cigarette Tar and Nicotine The table below lists amounts of tar per cigarette (milligrams) and amounts of nicotine (milligrams) from different cigarettes (from Data Set 16 “Cigarette Contents”). Tar 5.0 16 17.0 13.0 9.0 14 15.0 2.0 7.0 Nicotine 0.4 1 1.2 0.8 0.8 1 1.1 0.2 0.6 8. Pulse Rates The table lists pulse rates (beats per minute) from randomly selected females and randomly selected males (based on Data Set 1 “Body Data”). What is a major and fundamental flaw with this exercise? Female 66 56 82 78 86 88 56 36 84 76 Male 60 52 62 52 76 52 62 72 64 78 Linear Correlation Coefficient In Exercises 9–12, the linear correlation coefficient r is provided. Use Table 2-11 on page 77 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation? 9. Using the data from Exercise 5 “Forecast and Actual Temperatures,” the linear correlation coefficient is r = -0.475. 10. Using the data from Exercise 6 “Airport Data Speeds,” the linear correlation coefficient is r = 0.866. 11. Using the data from Exercise 7 “Cigarette Tar and Nicotine,” the linear correlation coefficient is r = 0.971. 12. Using the data from Exercise 8 “Pulse Rates,” the linear correlation coefficient is r = -0.076. As in Exercise 8, identify the major flaw with these data.
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