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.

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 (for example, the sample’s most livable city at #3 should be ranked 1, and the sample’s least livable at #192 should be ranked 20).

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Small Cities 17 18 3 10 13 92 17 111 124 69 Large Cities 19 47 85 00 8 178 116 120 14 75 192