Rank Correlation Use the ranks from Exercise 1 to find the value of the rank correlation coefficient. Also, use a 0.05 significance level and find the critical value of the rank correlation coefficient. What do you conclude about correlation?

A marketing researcher analyzed advertising budget vs. monthly sales revenue for small retail stores and found that typically the stores that spent more on advertising saw higher sales revenues. However, the relationship wasn't perfect - some stores advertised more but saw fewer sales due to poor location, customer preferences, or bad timing. Which of the following is the most likely value for the correlation coefficient $r$ between advertising budget and sales revenue?

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 α = 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.)

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.

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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 α = 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.)

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?

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 α = 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.)

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)?

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.