LetX equal the number of milliliters of a liquid in a

Chapter 8, Problem 2E

(choose chapter or problem)

Let \(X\) equal the number of milliliters of a liquid in a bottle that has a label volume of \(350 \mathrm{ml}\). Assume that the distribution of \(X\) is \(N(\mu, 4)\). To test the null hypothesis \(H_{0}\) : \(\mu=355\) against the alternative hypothesis \(H_{1}: \mu<355\), let the critical region be defined by \(C=\{\bar{x}: \bar{x} \leq 354.05\}\), where \(\bar{x}\) is the sample mean of the contents of a random sample of \(n=12\) bottles.

(a) Find the power function \(K(\mu)\) for this test.

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

(c) Find the values of \(K(354.05)\) and \(K(353.1)\), and sketch the graph of the power function.

(d) Use the following 12 observations to state your conclusion from this test:

(e) What is the approximate \(p\)-value of the test?

Equation Transcription:

 :  

 

 

 

 

Text Transcription:

X

N(mu,4)

H_0 : =355

H_1:<355

C={bar x: bar x < or = 354.05}

H_1:<715

C={bar x:bar x < or = 668.94}

Bar x

n=25

n=12

K(mu)

K(354.05)

K(353.1)

p