Aphid infestation of fruit trees can be controlled either byspraying with pesticide or

Chapter 7, Problem 53

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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 \(\mu_i=\) the true average yield (bushels/tree) after receiving the i th treatment. Then

                                           \(\theta=\frac{1}{3}\left(\mu_1+\mu_2+\mu_3\right)-\mu_4\)

measures the difference in true average yields between treatment with pesticides and treatment with ladybugs. When \(n_1, n_2, n_3\), and \(n_4\) are all large, the estimator \(\hat{\theta}\) obtained by replacing each \(\mu_i\) by \(\bar{X}_i\) is approximately normal. Use this to derive a large-sample \(100(1-\alpha) \%\) CI for \(\theta\), and compute the 95% interval for the given data.

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