rofessor Cornish studied rainfall cycles and sunspot cycles. (Reference: Australian Journal of Physics, Vol. 7, pp. 334-346.) Part of the data include amount of rain (in mm) for 6-day intervals. The following data give rain amounts for consecutive 6-day intervals at Adelaide, South Australia. 7 28 7 1 69 3 1 4 22 7 16 4 54 160 60 73 27 3 3 1 7 144 107 4 91 44 1 8 4 22 4 59 116 52 4 155 42 24 11 43 3 24 19 74 26 63 110 39 34 71 52 39 8 0 15 2 14 9 1 2 4 9 6 10
rofessor Cornish studied rainfall cycles and sunspot cycles. (Reference: Australian Journal of Physics, Vol. 7, pp. 334-346.) Part of the data include amount of rain (in mm) for 6-day intervals. The following data give rain amounts for consecutive 6-day intervals at Adelaide, South Australia.
| 7 | 28 | 7 | 1 | 69 | 3 | 1 | 4 | 22 | 7 | 16 | 4 | 54 | 160 |
| 60 | 73 | 27 | 3 | 3 | 1 | 7 | 144 | 107 | 4 | 91 | 44 | 1 | 8 |
| 4 | 22 | 4 | 59 | 116 | 52 | 4 | 155 | 42 | 24 | 11 | 43 | 3 | 24 |
| 19 | 74 | 26 | 63 | 110 | 39 | 34 | 71 | 52 | 39 | 8 | 0 | 15 | 2 |
| 14 | 9 | 1 | 2 | 4 | 9 | 6 | 10 |
(i) Find the
(ii) Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B a value below the median. Test the sequence for randomness about the median at the 5% level of significance.
(b) Find the number of runs R, n1, and n2. Let n1 = number of values above the median and n2 = number of values below the median.
| R | |
| n1 | |
| n2 |
(c) In the case, n1 > 20, we cannot use Table 10 of Appendix II to find the critical values. Whenever either n1 or n2 exceeds 20, the number of runs R has a distribution that is approximately normal, as follows.
We convert the number of runs R to a z value, and then use the
| z = |
|
(d) The critical values of a normal distribution for a two-tailed test with level of significance α = 0.05 are -1.96 and 1.96 (see Table 5(c) of Appendix II). Reject H0 if the sample test statistic z ≤ -1.96 or if the sample test statistic z ≥ 1.96. Otherwise, do not reject H0.
| Sample z ≤ -1.96 | -1.96 < sample z < 1.96 | Sample z ≥ 1.96 |
|---|---|---|
| Reject H0 | Fail to reject H0 | Reject H0 |
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