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:

Use the Wilcoxon test to decide whether one technique gives on average a different value than the other technique for this type of material.

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Sample GraviimetTic 54.7 58.5 66.8 46.1 Spectrophotometric55.0 55.7 62.9 45.5 Sample 6 52.3 74.3 92.5 40.2 Spectrophotometric 51.1 75.4 89.6 38.4 12 Gravimetric Sample 9 10 Gravimetric 87.3 74.8 63.2 68.5 Spectrophotometrie 86.8 725 62.3 66.0