Let X be N(?, 100). To test H0: ? = 80 against H1: ? > 80,

Chapter 8, Problem 4E

(choose chapter or problem)

Let \(X\) be \(N(\mu, 100)\). To test \(H_{0}: \mu=80\) against \(H_{1}: \mu>80\), let the critical region be defined by \(C=\) \(\left\{\left(x_{1}, x_{2}, \ldots, x_{25}\right): \bar{x} \geq 83\right\}\), where \(\bar{x}\) is the sample mean of a random sample of size \(n=25\) from this distribution.

(a) What is the power function \(K(\mu)\) for this test?

(b) What is the significance level of the test?

(c) What are the values of \(K(80), K(83)\), and \(K(86)\) ?

(d) Sketch the graph of the power function.

(e) What is the \(p\)-value corresponding to \(\bar{x}=83.41\)?

Equation Transcription:

 

 

 

 ,

 

 

 

 ?

Text Transcription:

X  

N(mu,100)  

H_0:=80  

H_1:>80

C= {x_1,x_2,…,x_25): bar x > or = 83}

Bar x  

n=25  

K(mu)

K(80),K(83)

K(86)  

p

Bar

x=83.41