Regression If the methods of this section are used with paired sample data, and the

Regression If the methods of this section are used with paired sample data, and the conclusion is that there is sufficient evidence to support the claim of a correlation between the two variables, can we use the methods of Section 103 to find the regression equation that can be used for predictions? Why or why not?

Level of Measurement Which of the levels of measurement (nominal, ordinal, interval, ratio) describe data that cannot be used with the methods of rank correlation? Explain.

Notation What do r, r s , , and s denote? Why is the subscript s used? Does the subscript s represent the same standard deviation s introduced in Section 33?

. Efficiency Refer to Table 132 in Section 131 and identify the efficiency of the rank correlation test. What does that value tell us about the test?

In Exercises 5 and 6, use the scatterplot to find the value of the rank correlation coefficient r s and the critical values corresponding to a 0.05 significance level used to test the null hypothesis of s = 0 . Determine whether there is a correlation.Distance/Time Data for a Dropped Object d

In Exercises 5 and 6, use the scatterplot to find the value of the rank correlation coefficient r s and the critical values corresponding to a 0.05 significance level used to test the null hypothesis of s = 0 . Determine whether there is a correlation.. Altitude/Time Data for a Descending Aircraft d

Testing for Rank Correlation. In Exercises 712, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of = 0.05 .Are the Best Televisions the Most Expensive? The following table lists overall quality scores and prices of 40inch LCD televisions (based on data from Consumer Reports). Do these data suggest that you can get better quality by spending more? Quality score 74 71 68 65 63 62 57 Price (dollars) 2700 3000 3800 2300 2000 1300 1400

Testing for Rank Correlation. In Exercises 712, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of = 0.05 .Are the Best Paints the Most Expensive? The following table lists overall quality scores and prices for a gallon of exterior paints (based on data from Consumer Reports). Do these data suggest that you can get better quality by spending more? Quality score 90 87 82 78 62 56 23 19 Price (dollars) 27 32 19 15 39 24 15 18

Testing for Rank Correlation. In Exercises 712, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of = 0.05 .Judges of Marching Bands Two judges ranked seven bands in the Texas state finals competition of marching bands (Coppell, Keller, Grapevine, Dickinson, Poteet, Fossil Ridge, Heritage), and their rankings are listed below (based on data from the University Interscholastic League). Test for a correlation between the two judges. Do the judges appear to rank about the same or are they very different? Band Cpl Klr Grp Dck Ptt FR Her First judge 1 3 4 7 5 6 2 Second judge 6 4 5 1 3 2 7

Testing for Rank Correlation. In Exercises 712, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of = 0.05 . Judges of Marching Bands In the same competition described in Exercise 9, a third judge ranked the bands with the results shown below. Test for a correlation between the first and third judges. Do the judges appear to rank about the same or are they very different? Band Cpl Klr Grp Dck Ptt FR Her First judge 1 3 4 7 5 6 2 Third judge 3 4 1 5 7 6 2

Testing for Rank Correlation. In Exercises 712, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of = 0.05 . Measuring Seals from Photos Listed below are the overhead widths (in cm) of seals measured from photographs and the weights of the seals (in kg). The data are based on Mass Estimation of Weddell Seals Using Techniques of Photogrammetry, by R. Garrott of Montana State University. The purpose of the study was to determine if weights of seals could be determined from overhead photographs. Is there sufficient evidence to conclude that there is a correlation between overhead widths of seals from photographs and the weights of the seals? Overhead width 7.2 7.4 9.8 9.4 8.8 8.4 Weight 116 154 245 202 200 191

Testing for Rank Correlation. In Exercises 712, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of = 0.05 .Crickets and Temperature The association between the temperature and the number of times a cricket chirps in 1 min was studied. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in degrees Fahrenheit (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 relationship between the number of chirps in 1 min and the temperature? Chirps in 1 min 882 1188 1104 864 1200 1032 960 900 Temperature ( F ) 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6

Appendix B Data Sets. In Exercises 1316, use the data from Appendix B to test for rank correlation with a 0.05 significance level.Blood Pressure Refer to the measured systolic and diastolic blood pressure measurements of 40 randomly selected males in Data Set 1 in Appendix B and test the claim that among men, there is a correlation between systolic blood pressure and diastolic blood pressure.

Appendix B Data Sets. In Exercises 1316, use the data from Appendix B to test for rank correlation with a 0.05 significance level.. IQ and Brain Volume Refer to Data Set 6 in Appendix B and use the paired data consisting of brain volume ( cm 3 ) and IQ score.

Appendix B Data Sets. In Exercises 1316, use the data from Appendix B to test for rank correlation with a 0.05 significance level. Flight Delays Refer to Data Set 15 in Appendix B and use the departure delay times and the arrival delay times

Appendix B Data Sets. In Exercises 1316, use the data from Appendix B to test for rank correlation with a 0.05 significance level.. Earthquakes Refer to Data Set 16 in Appendix B and use the magnitudes and depths from the earthquakes.

Finding Critical Values An alternative to using Table A9 to find critical values for rank correlation is to compute them using this approximation: r s = t 2 t 2 + n 2 Here t is the critical t value from Table A3 corresponding to the desired significance level and n 2 degrees of freedom. Use this approximation to find critical values of r s for the following cases. Are the resulting approximations close to the values from Table A9? a. n = 8 , = 0.05 b. n = 30 , = 0.01