Aphid infestation of fruit trees can be controlled either by spraying with pesticide or by inundation with ladybugs. In a particular area, four different groves of fruit trees are selected for experimentation. The first three groves are sprayed with pesticides 1, 2, and 3, respectively, and the fourth is treated with ladybugs, with the following results on yield:

Let µi = the true average yield (bushels/tree) after receiving the ith treatment. Then
σ = 1/3 (µ1 + µ2 + µ3) - µ4
measures the difference in true average yields between treatment with pesticides and treatment with ladybugs. When n1, n2, n3, and n4 are all large, the estimator σ obtained by replacing each µi by Xi is approximately normal. Use this to derive a large-sample 100(1 - α)% CI for u, and compute the 95% interval for the given data.

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n-= Number Treatment of Trees (Bushels/Tree), 1.5 1.3 1.8 1.6 100 90 100 120 10.5 10.0 10.1 10.7 3 4