In Biometrics (1990, Vol. 46, pp. 673€“87), the authors analyzed the circumference of five orange trees (labeled as A€“E) measured on seven occasions (x_i).

(a) Compare the mean increase in circumference in periods 1 to 2 to the mean increase in periods 2 to 3. The increase is the difference in circumference in the two periods. Are these means significantly different at α = 0.10?

(b) Is there evidence that the mean increase in period 1 to period 2 is greater than the mean increase in period 6 to period 7 at α = 0.05?

(c) Are the assumptions of the test in part (a) violated because the same data (period 2 circumference) are used to calculate both mean increases?

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Tree x, x, A 30 58 87 115 120 142 145 33 156 172 203 203 B 69 111 30 51 75 108 115 139 140 112 167 209 214 D 32 62 179 30 49 81 125 142 174 177