Describe the ranges of the Spearman rank correlation coefficient and the Pearson correlation coefficient.

In Exercises 5 and 6, use the scatterplot to find the value of the rank correlation coefficient and the critical values corresponding to a 0.05 significance level used to test the null hypothesis of . Determine whether there is a correlation.

Altitude and Temperature Shown below is a scatterplot of altitudes (thousands of feet) and outside air temperatures (degrees Fahrenheit) recorded by the author during a Delta flight from New Orleans to Atlanta.

Testing for Rank Correlation

In Exercises 7–12, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of α = 0.05.

Colombian Coffee The following table lists quality rankings and costs (dollars) for a pound of different brands of Colombian coffee (based on data from Consumer Reports). Lower values of the quality rankings correspond to better coffee. Do the more expensive brands appear to have better quality?

Testing for Rank Correlation

In Exercises 7–12, use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of α = 0.05.

Computers The following table lists quality rankings and costs (dollars) for different brands of laptop computers with 12 in. or 13 in. screens (based on data from Consumer Reports). Lower values of the quality rankings correspond to better computers. Do the more expensive brands appear to have better quality?

Appendix B Data Sets

In Exercises 29–32, use the data from Appendix B to construct a scatterplot, find the value of the linear correlation coefficient r, and find either the P-value or the critical values of r from Table A-6 using a significance level of α = 0.05. Determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

Taxis Repeat Exercise 15 using all of the time/tip data from the 703 taxi rides listed in Data Set 32 “Taxis” from Appendix B. Compare the results to those found in Exercise 15.

1. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases? What if the variables have a negative linear correlation?

2. Describe the range of values for the correlation coefficient.

3. What does the sample correlation coefficient r measure? Which value indicates a stronger correlation: r =0.918 or r =- 0.932? Explain your reasoning.

6. Discuss the difference between r and p.