For the past 16 years, the yields of wheat (in tons) grown on a plot at...
For the past 16 years, the yields of wheat (in tons) grown on a plot at Rothamsted Experimental Station (England) are shown below. The sequence is by year.
| 1.4 | 1.3 | 0.7 | 1.9 | 2.1 | 3.4 | 3.1 | 1.9 | 2.8 | 2.4 | 2.5 | 2.2 |
| 2.4 | 2.6 | 1.7 | 3.7 |
Use level of significance 5% to test for randomness about the median.
(a) State the test used.
spearman correlation testsign test rank-sum testruns test
(b) Give ?.
State the null and alternate hypotheses.
Ho: The numbers are randomly mixed about the median. H1: The numbers are not randomly mixed about the median.Ho: The numbers are not randomly mixed about the median. H1: The numbers are randomly mixed about the median. Ho: The numbers are not randomly mixed about the mean. H1: The numbers are randomly mixed about the mean.Ho: The numbers are randomly mixed about the mean. H1: The numbers are not randomly mixed about the mean.
(c) Find the sample test statistic.
(d) For the sign test, rank-sum test, and Spearman correlation
coefficient test, find the P-value of the sample test
statistic. For the runs test of randomness, find the critical
values from Table 10 of Appendix II.
| c1 | |
| c2 |
(e) Conclude the test.
At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is sufficient evidence that the sequence of wheat yields is not random about the median.Fail to reject the null hypothesis, there is sufficient evidence that the sequence of wheat yields is not random about the median. Fail to reject the null hypothesis, there is insufficient evidence that the sequence of wheat yields is not random about the median.Reject the null hypothesis, there is insufficient evidence that the sequence of wheat yields is not random about the median.
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