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. x 141 140 197 224 54 175 257 72 172 y 176 142 217 125 43 245 218 35 147 x 218 265 110 193 180 190 94 8 66 y 208 218 100 170 245 117 140 99 97 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. What is the level of significance? Compute the sample test statistic. (Round your answer to two decimal places.) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.