5. Both a gravimetric and a spectrophotometric method are under consideration for determining phosphate content of a particular material. Twelve samples of the material are obtained, each is split in half, and a determination is made on each half using one of the two methods, resulting in the following data:
Sample 1 2 3 4 Gravimetric 54.7 58.5 66.8 46.1 Spectrophotometric 55.0 55.7 62.9 45.5 Sample 5 6 7 8 Gravimetric 52.3 74.3 92.5 40.2 Spectrophotometric 51.1 75.4 89.6 38.4 Sample 9 10 11 12 Gravimetric 87.3 74.8 63.2 68.5 Spectrophotometric 86.8 72.5 62.3 66.0 Use the Wilcoxon test to decide whether one technique gives on average a different value than the other technique for this type of material.