The following data were obtained in an experiment designed to check whether there is a systematic difference in the weights obtained with two different scales:

Use the paired \(t\) test at the 0.05 level of significance to try to establish that the mean difference of the weights obtained with the two scales is nonzero.

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Weight in grams Scale I Scale II Rock Specimen 1 11.23 11.27 Rock Specimen 2 14.36 14.41 Rock Specimen 3 8.33 8.35 Rock Specimen 4 10.50 10.52 Rock Specimen 5 23.42 23.41 Rock Specimen 6 9.15 9.17 Rock Specimen 7 13.47 13.52 Rock Specimen 8 6.47 6.46 Rock Specimen 9 12.40 12.45 Rock Specimen 10 19.38 19.35