The following data are paired by date. Let x and y be random variables representing wind direction at 5 _A.M. and 5 _P.M., respectively (units are degrees on a compass, with 0° representing true north). The readings were taken at seeding level in a cloud seeding experiment.

A random sample of days gave the following information.

Use the sign test with a 5% level of signi­ficance to test the claim that the distributions of wind directions at 5 _A.M. and 5 _P.M. are different. Interpret the results.

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xi 177 140 197 224 49 175 257 72 172 у| 142 142 217 125 53 245 218 35 147 x214 265 110 193 180 190 948 93 y 205 218 100 170 245 117140 99 60