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Chapter 13: Q2BSC (page 597)
Rank Sum After ranking the combined list of professor evaluations given in Exercise 1, find the sum of the ranks for the female professors.
The sum of the ranks corresponding to the female professors is 163.
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CPI and the Subway Use CPI/subway data from the preceding exercise to test for a correlation between the CPI (Consumer Price Index) and the subway fare.
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\(\rho \)= 0. Determine whether there is a correlation.
Altitude,Time Data for a Descending Aircraft
Using Nonparametric Tests. In Exercises 1–10, use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.
Job Stress and Income Listed below are job stress scores and median annual salaries (thousands of dollars) for various jobs, including firefighters, airline pilots, police officers, and university professors (based on data from “Job Rated Stress Score” from CareerCast.com). Do these data suggest that there is a correlation between job stress and annual income? Does it appear that jobs with more stress have higher salaries?
Stress | 71.59 | 60.46 | 50.82 | 6.94 | 8.1 | 50.33 | 49.2 | 48.8 | 11.4 |
Median Salary | 45.6 | 98.4 | 57 | 69 | 35.4 | 46.1 | 42.5 | 37.1 | 31.2 |
Using the Runs Test for Randomness. In Exercises 5–10, use the runs test with a significance level of\(\alpha \)= 0.05. (All data are listed in order by row.)
Newspapers Media experts claim that daily print newspapers are declining because of Internet access. Listed below are the numbers of daily print newspapers in the United States for a recent sequence of years. First find the median, then test for randomness of the numbers above and below the median. What do the results suggest?
1611 | 1586 | 1570 | 1556 | 1548 | 1533 | 1520 | 1509 | 1489 | 1483 | 1480 |
1468 | 1457 | 1456 | 1457 | 1452 | 1437 | 1422 | 1408 | 1387 | 1382 |
Using the Mann-Whitney U Test The Mann-Whitney U test is equivalent to the Wilcoxon rank-sum test for independent samples in the sense that they both apply to the same situations and always lead to the same conclusions. In the Mann-Whitney U test we calculate
\(z = \frac{{U - \frac{{{n_1}{n_2}}}{2}}}{{\sqrt {\frac{{{n_1}{n_2}\left( {{n_1} + {n_2} + 1} \right)}}{{12}}} }}\)
Where
\(U = {n_1}{n_2} + \frac{{{n_1}\left( {{n_1} + 1} \right)}}{2} - R\)
and R is the sum of the ranks for Sample 1. Use the student course evaluation ratings in Table 13-5 on page 621 to find the z test statistic for the Mann-Whitney U test. Compare this value to the z test statistic found using the Wilcoxon rank-sum test.
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