#32
Is there a relation between police protection and fireprotection? A random sample of large population areas gave thefollowing information about the number of local police and thenumber of local fire-fighters (units in thousands). (Reference:Statistical Abstract of the United States.)
| Area | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| Police | 10.8 | 13.3 | 17.0 | 16.3 | 7.6 | 3.2 | 5.3 | 15.4 | 2.7 | 4.7 | 4.1 | 6.1 | 5.6 |
| Firefighters | 3.1 | 2.5 | 4.8 | 2.9 | 3.3 | 1.2 | 2.4 | 3.4 | 1.0 | 1.5 | 2.3 | 2.7 | 0.9 |
Use a 5% level of significance to test the claim that there is amonotone relationship (either way) between the ranks of number ofpolice and number of firefighters.
(a) Rank-order police using 1 as the largest data value. Alsorank-order firefighters using 1 as the largest data value. Thenconstruct a table of ranks to be used for a Spearman rankcorrelation test.
| Area | Police
Rank x | Firefighters
Rank y | d = x -y | d2 |
1
2
3
4
5
6
7
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9
10
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12
13
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Σd2 = |
(c) Compute the sample test statistic. (Use 3 decimalplaces.)
