4. Sign Test: Wind Direction 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. (Reference: Proceedings of the National Academy of Science, Vol. 68, pp. 649–652.) A random sample of days gave the following information.

x 177 140 197 224 49 175 257 72 172 y 142 142 217 125 53 245 218 35 147 x 214 265 110 193 180 190 94 8 93 y 205 218 100 170 245 117 140 99 60 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.