Assume that SAT mathematics scores of students who attend

Chapter 8, Problem 3E

(choose chapter or problem)

Assume that SAT mathematics scores of students who attend small liberal arts colleges are \(N(\mu, 8100)\). We shall test \(H_{0}: \mu=530\) against the alternative hypothesis \(H_{1}: \mu<530\). Given a random sample of size \(n=36\) SAT mathematics scores, let the critical region be defined by \(C=\{\bar{x}: \bar{x} \leq 510.77\}\), where \(\bar{x}\) is the observed mean of the sample.

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

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

(c) What is the value of \(K(510.77)\) ?

(d) Sketch the graph of the power function.

(e) What is the \(p\)-value associated with (i) \\bar{x}=507.35\); (ii) \(\bar{x}=497.45\)?

Equation Transcription:

 

 

 

  

 

Text Transcription:

N(mu,8100)

H_0:=530

H_1:<530

n=36

C={bar  x: bar x≤510.77}

Bar x

K(mu)

K(510.77)

p

Bar x=507.35

Bar x=497.45