Homework Sourse1An engineer is interested in testing the fill volume of two
1.An engineer is interested in testing the fill volume of two different machines. Two random samples of size 5 measurements were selected to determine if there is a significance difference between their mean fill volumes. The measurements (in ounces) are shown in the accompanying table. State your conclusion using the Wilcoxon Rank-Sum Test at ?=0.05.
Machine#1 Machine#2
16.03 16.00
16.04 15.97
16.05 15.95
16.02 15.99
15.96 15.97
Solution
16.03
16.05
15.96
W value
sum of ranks
z value
Result 1 - Z-value
The Z-value is -1.7529. However, the size of N (5) is not large enough for the distribution of the Wilcoxon W statistic to form a normal distribution. Therefore, it is not possible to calculate an accurate p-value.
| Treatment I | Treatment II | Sign | Abs | R | Sign R |
| 16.03 | 16 | 1 | 0.03 | 3 | 3 |
| 16.04 | 15.97 | 1 | 0.07 | 4 | 4 |
| 16.05 | 15.95 | 1 | 0.1 | 5 | 5 |
| 16.02 | 15.99 | 1 | 0.03 | 2 | 2 |
| 15.96 | 15.97 | -1 | 0.01 | 1 | -1 |
| W value | 1 | ||||
| Mean diff | 0.05 | ||||
| sum of ranks | 14 | ||||
| sum of neg ranks | 1 | ||||
| z value | -1.7529 | ||||
| Sample size | 5 | ||||
| Result 1 - Z-value |
