16. A committee of students wanted to know whether student activity fees were being charged fairly. To determine whether commuting and resident students differed in their use of campus activities, the following sample data were collected pertaining to the number of campus activities/clubs each student joined: Commuters 6 Campus Residents 9 2 2148332115 12 4 11 9 8 6 6 11 12 11 10 7 9 Applying the Mann-Whitney U test, test the null hypothesis of no difference between commuters and campus residents with respect to use of campus activities. 123 A B C Small Cities (rank) 17 6.5 D E Large Cities (rank) FL G H 19 9 combined 3 3 18 8 00 47 10 8 4 3 1 85 13 10 5 10 3 8 2 13 1234 60 13 4 st 178 19 14 5 7 92 14 116 17 17 6.5 8 00 17 6.5 120 16 17 6.5 9 111 15 14 5 18 8 10 124 18 75 12 19 9 11 69 11 192 20 47 10 12 87 123 69 11 13 75 12 15 14 16 | U = NN + - N (N+1) 85 13 2 -R 92 14 111 15 17 18 =(10)(10)+ 10(10+1) 116 16 -87 120 2 17 19 124 18 100+55-87 20 178 19 21 = 68 192 20 20 22 N (N+1) 23 U = NN+ 24 2 -R 25 10(10+1) 26 =(10)(10)+ -123 2 27 28 =100+55-123 29 =32 30 31 alpha = .05 32 n1,n2 = 10,10 33 34 Critical U value: 23 (from U table) Conclusion: 32 > 23, reject the null 35 A major national magazine has ranked 200 American cities in terms of their livability. A social researcher selects 10 large cities and 10 small cities at random and wishes to test whether there is a difference in livability based on city size. The magazine's rankings (among the full list) of the cities that were selected are given in the following table: ice Activity 9 309, Kemmerer Small cities Large cities 17 19 18 47 3 85 10 8 13 178 92 116 17 120 111 14 124 75 69 192 Applying the Mann-Whitney U test, determine whether there is a significant difference between large and small cities with respect to livability. Note that the magazine's rankings should be re-ranked from 1 (most livable) to 20 (least livable) to reflect the order within the sample (e.g., the sample's most livable city at #3 should be ranked 1, and the sample's least livable at #192 should be ranked 20).