Ch 11 - 29E

Chapter 11, Problem 29E

(choose chapter or problem)

Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) be as given in Exercise 11.28. Suppose that we have an additional set of independent random variables \(W_{1}, W_{2}, \ldots, W_{m}\), where \(W_{1}\) is normally distributed with \(E\left(W_{1}\right)=V_{0}+y_{1} c_{1}\) and \(V\left(W_{1}\right)=o^{2}\), for i = 1, 2, . . . ,m. Construct a test of \(H_{0}: \beta_{1}=y_{1}\) against the \(H_{a}: \beta_{1} \neq y_{1}^{6}\)

Equation transcription:

Text transcription:

Y{1}, Y{2}, \ldots, Y{n}

W{1}, W{2}, \ldots, W{m}

W{1}

E\left(W{1}\right)=V{0}+y{1} c{1}

V\left(W{1}\right)=o^{2}

H_{0}: beta_{1}=y{1}

H_{a}: beta{1} \neq y{1}^{6}