1. What is the rank correlation test used for? (p. 14-44)

2. Describe three advantages and one disadvantage to using the rank correlation test. (p. 14-45)

3. Is the rank correlation test used for dependent or independent samples? Explain. (p. 14-46)

4. The test statistic is based on the calculation of the sum of the squared differences of the ranks, . Explain the steps involved in calculating . (p. 14-45)

5. What is the general form for the hypotheses for the rank correlation test? (p. 14-46)

6. In Chapter 13, we found that linear regression was not appropriate when the relationship between the variables was not linear. Does this condition also hold true for the rank correlation test? (p. 14-48)

7. Suppose that two Olympic judges each rank five figure skaters from 1 through 5, and their rankings are exactly the same. What is the value of the sum of the squared differences ? What is the value of the test statistic ? (p. 14-45, 14-46)

8. Based on your answer to Exercise 7, what is the conclusion of the rank correlation test for association between the two judges? Explain. (p. 14-47)

1. Rank the data within each sample, using our convention for handling ties.
2. Calculate the sum of the squared differences of the ranks, .
3. Compute the value of the test statistic

9.

10.

11.

12.

13. Use the data from Exercise 9 and level of significance .

14. Use the data from Exercise 10 and level of significance .

15. Use the data from Exercise 11 and level of significance .

16. Use the data from Exercise 12 and level of significance .

1. State the hypotheses.

2. Find the critical value and state the rejection rule.

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3. Calculate the test statistic .
4. State the conclusion and the interpretation.

17. Use the data and test statistic from Exercise 9, level of significance , and from Exercise 13.

18. Use the data and test statistic from Exercise 10, level of significance , and from Exercise 14.

19. Use the data and test statistic from Exercise 11, level of significance , and from Exercise 15.

20. Use the data and test statistic from Exercise 12, level of significance , and from Exercise 16.

21. Ranking the Presidents. A study asked a randomly selected group of liberal historians and a randomly selected group of conservative historians to rank the presidents of the United States since George Washington.¹² Interestingly, both groups agreed on the top five presidents, but the rankings were not exactly the same. The rankings for the top five are shown here. Test whether a rank correlation exists between the liberal ranks and the conservative ranks, using level of significance . Note that you need not calculate the ranks, as the ranks are given.

22. Best Countries for Business. The Web site www.doingbusiness.org publishes rankings on the best countries for doing business. The following data set represents a random sample of nations and their rankings in two categories: ease of doing business and ease of starting up a new business. Test whether a rank correlation exists between the two categories, using level of significance . Note that you need not calculate the ranks, as the ranks are given.

23. College Football. Different polls do not all show the same rankings for the best teams in college football. The table contains the points (calculated by votes received) for the top 24 teams for the 2013 season in the Associated Press (AP) poll and the USA Today poll. Test whether a rank correlation exists between the two polls, using level of significance .

24. Population and Area. Does an association exist between the size (in square miles) of a nation and the number of people who live in that nation (the population)? The following data set represents a random sample of 12 countries and their areas and populations. Test whether a rank correlation exists between area and population, using level of significance .

25. Video Game Ranking. GameRankings.com publishes summary statistics for reviews of video games. The following data set represents a random sample of video games and their average reviewer score for the PlayStation 3 platform and the Xbox 360 platform, as of January 23, 2009. Test whether a rank correlation exists between the two game platforms, using level of significance .

26. Environmental Scores. Greenpeace International publishes its rankings of the major manufacturers of electronics, according to their policies on toxic chemicals, recycling, and climate change. The following data set represents the scores received for a random sample of companies in Greenpeace's September 2008 report and their November 2008 report. Higher scores mean that the company is more environmentally responsible in these areas. Test whether a rank correlation exists between the two reports, using level of significance .

27. Community Colleges. The following data set represents the results of the Washington Monthly's ranking of the top 30 community colleges in the nation. Two rankings are provided: the first for overall quality and the second for tuition and fees. Test whether a rank correlation exists between the two variables, using level of significance . You need to calculate the ranks for the “tuition and fees” variable, but not for the “overall quality” variable.

28. Age and Weight. The relationship between age and weight is nonlinear, so that linear regression should not be used to test for the relationship. The Centers for Disease Control and Prevention published a case study regarding a particular child, recording the age and weight of this child at various intervals. Assume that the data set represents a random sample. Use the rank correlation test to test for a relationship between age and weight, using level of significance .

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29. Cigarettes and Bladder Cancer. A study examined the relationship between the number of cigarettes smoked and various types of cancer.¹³ The relationship between bladder cancer and the number of cigarettes may involve a nonlinear component. The following data set is a random sample of U.S. states, along with the number of deaths from bladder cancer per 100,000 people and the number of cigarettes smoked in hundreds per capita. Use the rank correlation test to test for a relationship between the number of deaths from bladder cancer and the per capita number of cigarettes smoked, using level of significance .