2. Non parametric test - Sign test for the following data
50,15,25,12,45,3,45,8,10,8,7,20,9,9,12
Median = 20, Significance Level `alpha=0.05` and One-tailed test
Solution:
Step-1:State the hypothesis
`H_0`: population median `>=` 20.
`H_1`: population median `<` 20.
Step-2: To perform the test, we count number of elements > 20 and number of elements < 20. We drop elements with value exactly 20.
In 3rd column, we put + if element is > 20, - if element is < 20 and n/a if element is = 20.
| # | A | Sign |
| 1 | 50 | + |
| 2 | 15 | - |
| 3 | 25 | + |
| 4 | 12 | - |
| 5 | 45 | + |
| 6 | 3 | - |
| 7 | 45 | + |
| 8 | 8 | - |
| 9 | 10 | - |
| 10 | 8 | - |
| 11 | 7 | - |
| 12 | 20 | n/a |
| 13 | 9 | - |
| 14 | 9 | - |
| 15 | 12 | - |
Step-3:
Number of plus sign = 4
Number of minus sign = 10
n = 4 + 10 = 14
Step-4:
p-value = BINOMDIST(4, 14, 0.5, TRUE) = 0.0898
Since the p-value(0.0898) > `alpha(0.05)` (one-tailed test), we can't reject the null hypothesis `H_0`.
This material is intended as a summary. Use your textbook for detail explanation.
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