Question
The following data are paired by date. Let x and y be random variables representing wind...
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 178 140 197 224 54 175 257 72 172 y 148 142 217 125 49 245 218 35 147 x 207 265 110 193 180 190 94 8 91 y 213 218 100 170 245 117 140 99 62 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? State the null and alternate hypotheses. H0: Distributions are the same. H1: Distributions are different. H0: Distributions are different. H1: Distributions are different. H0: Distributions are the same. H1: Distributions are the same. H0: Distributions are different. H1: Distributions are the same. Compute the sample test statistic. (Round your answer to two decimal places.) What sampling distribution will you use? Student's t normal chi-square uniform Find the P-value of the sample test statistic. (Round your answer to four decimal places.)
Homework Answers
Answer #1
H0: Distributions are the same
H1: Distributions are the different
Form the given data
| S.No. | X | Y | Diff = X-Y |
| 1 | 178 | 148 | 30 |
| 2 | 140 | 142 | -2 |
| 3 | 197 | 217 | -20 |
| 4 | 224 | 125 | 99 |
| 5 | 54 | 49 | 5 |
| 6 | 175 | 245 | -70 |
| 7 | 257 | 218 | 39 |
| 8 | 72 | 35 | 37 |
| 9 | 172 | 147 | 25 |
| 10 | 207 | 213 | -6 |
| 11 | 265 | 218 | 47 |
| 12 | 110 | 100 | 10 |
| 13 | 193 | 170 | 23 |
| 14 | 180 | 245 | -65 |
| 15 | 190 | 117 | 73 |
| 16 | 94 | 140 | -46 |
| 17 | 8 | 99 | -91 |
| 18 | 91 | 62 | 29 |
| S+ = | number of +ve signs |
| = | 11 |
| S- = | 7 |
Thus we conclude that Distributions are different
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