64. 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 rst three groves are sprayed with pesticides 1, 2, and 3, respectively, and the fourth is treated with ladybugs, with the following results on yield:

ni

(number (bushels/

Treatment of trees) tree) si 1 100 10.5 1.5 2 90 10.0 1.3 3 100 10.1 1.8 4 120 10.7 1.6 Let mi  the true average yield (bushels/tree) after receiving the ith treatment. Then 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 u 

1 3

1m1  m2  m3 2  m4 xi

x2i

xi  8.08100  1.37813 estimator obtained by replacing each mi by is approximately normal. Use this to derive a largesample 100(1  a)% CI for u, and compute the 95% interval for the given data.