In the next column are the lengths (in mm) of furniture dowels recorded as part of an ongoing quality control program. Listed are the measurements made on thirty samples (each of size 4) taken in order from the assembly line. Is the variation in the sample averages random with respect to the number of runs up and down? Do an appropriate hypothesis test at the α = 0.05 level of significance.

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Sample yı уг уз У4 у 1 46.1 44.4 45.3 44.2 45.0 2 46.0 45.4 42.5 44.4 44.6 3 44.3 44.0 45.4 43.9 44.4 4 44.9 43.7 45.2 44.8 44.7 5 43.0 45.3 45.9 43.8 44.5 6 46.0 43.2 44.4 43.7 44.3 7 46.0 44.6 45.4 46.4 45.6 8 46.1 45.5 45.0 45.5 45.5 9 42.8 45,1 44.9 44.3 44.3 10 45.0 46.7 43.0 44.8 44.9 11 45.5 44.5 45.1 47.1 45.6 12 45.8 44.6 44.8 45.1 45.1 13 45.1 45.4 46.0 45.4 45.5 14 44.6 43.8 44.2 43.9 44.1 15 44.8 45.5 45.2 46.2 45.4 16 45.8 44.1 43.3 45.8 44.8 17 44.1 44.8 46.1 45.5 45.1 18 44.5 43.6 45.1 46.9 45.0 19 45.2 43.1 46.3 46.4 45.3 20 45.9 46.8 46.8 45.8 46.3 21 44.0 44.7 46.2 45.4 45.1 22 43.4 44.6 45.4 44.4 44.5 23 43.1 44.6 44.5 45.8 44.5 24 46.6 43.3 45.1 44.2 44.8 25 46.2 44.9 45.3 46.0 45.6 26 42.5 43.4 44.3 42.7 43.2 27 43.4 43.3 43.4 43.5 43.4 28 42.3 42.4 46.6 42.3 43.4 29 41.9 42.9 42.0 42.9 42.4 30 43.2 43.5 42.2 44.7 43.4