Sunnydale Farms markets an all-purpose fertilizer that is supposed to contain, by weight, 15% potash (K2O). Samples were taken daily in October from three bags chosen at random as they came off the filling machine. Tabulated on the right are the K2O percentages recorded. Calculate the range (= ymax ˆ’ ymin) for each sample. Use Theorem 14.6.1 to test whether the variation in the ranges can be considered random with respect to the number of runs up and down.

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Date y 2 y3 10/1 16.1 14.4 15.3 10/2 16.0 16.4 13.5 10/3 14.3 14.0 15.4 10/4 14.8 13.1 15.2 10/5 12.0 15.4 16.4 10/15 16.3 13.3 15.3 10/16 17.4 13.8 14.3 10/17 13.5 11.0 15.4 10/18 15.6 9.2 18.9 10/19 16.3 17.6 20.5 10/8 16.4 12.3 14.2 109 16.9 14.2 15.8 10/10 17.2 16.0 14.9 10/1 10.6 15.3 10/12 15.0 19.2 3 10/22 14.3 15.6 17.0 10/23 15.4 15.3 15.4 10/24 14.3 14.4 18.6 14.9 10/25 13.9 14.9 14.0 10.010/26 15.2 15.5 14.2