(a) Devise a test statistic for H0: ? = 0 versus H1: ? ?

Chapter 11, Problem 44E

(choose chapter or problem)

 Consider the no-intercept model \(Y=\beta x+\epsilon\) with the \(\epsilon^{\prime} \mathrm{s}\) NID \(\left(0,\ \sigma^2\right)\) The estimate of  \(\sigma^{2}\) is \(s^{2}=\Sigma_{t=1}^{n}\left(y_{i}-\hat{\beta} x_{i}\right)^{2} /(n-1)\) and \(V(\hat{\beta})=\sigma^{2} / \Sigma_{i=1}^{n} x_{i}^{2}\)

        

 Devise a test statistic for \(H_0\ :\ \beta=0\) versus \(H_1:\ \beta\ne0\).Apply the test in (a) to the model from Exercise 11-22.

Equation Transcription:

Text Transcription:

Y=betax+epsilon

epsilon's

(0,sigma^2)

sigma^2

s^2=Sigma_t=1^n(y_i-beta hat x_i)^2/(n-1)

V(beta hat)=sigma^2/Sigma_i=1^n x_i^2

H_0:beta=0

H_1:beta not=0