Let X equal the yield of alfalfa in tons per acre per

Chapter 8, Problem 5E

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Let \(X\) equal the yield of alfalfa in tons per acre per year. Assume that \(X\) is \(N(1.5,0.09)\). It is hoped that a new fertilizer will increase the average yield. We shall test the null hypothesis \(H_{0}: \mu=1.5\) against the alternative hypothesis \(H_{1}: \mu>1.5\). Assume that the variance continues to equal \(\sigma^{2}=0.09\) with the new fertilizer. Using \(\bar{X}\), the mean of a random sample of size \(n\), as the test statistic, reject \(H_{0}\) if \(\bar{x} \geq c\). Find \(n\) and \(c\) so that the power function \(K(\mu)=P(\bar{X} \geq c: \mu)\) is such that \(\alpha=K(1.5)=0.05\) and \(K(1.7)=0.95\).