(In some of the exercises that follow, we must

Chapter 8, Problem 12E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Let \(X\) and \(Y\) denote the respective lengths of male and female green lynx spiders. Assume that the distributions of \(X\) and \(Y\) are \(N\left(\mu_{X}, \sigma_{X}^{2}\right)\) and \(N\left(\mu_{Y}, \sigma_{Y}^{2}\right)\), respectively, and that \(\sigma_{Y}^{2}>\sigma_{X}^{2}\). Thus, use the modification of \(Z\) to test the hypothesis \(H_{0}: \mu_{X}-\mu_{Y}=0\) against the alternative hypothesis \(H_{1}: \mu_{X}-\mu_{Y}<0\).

(a) Define the test statistic and a critical region that has a significance level of \(\alpha=0.025\).

(b) Using the data given in Exercise 7.2-5, calculate the value of the test statistic and state your conclusion.

(c) Draw two box-and-whisker diagrams on the same figure. Does your figure confirm the conclusion of this exercise?

Equation Transcription:

 

 

 

 

 


Text Transcription:

X  

Y  

N(mu_X, sigma_X^2)  

N(mu_Y, sigma_Y^2)

sigma_Y^2>sigma_X^2  

Z  

H_0:mu_X-mu_Y=0  

H_1:mu_X-m_Y<0  

alpha=0.025

Questions & Answers

QUESTION:

Let \(X\) and \(Y\) denote the respective lengths of male and female green lynx spiders. Assume that the distributions of \(X\) and \(Y\) are \(N\left(\mu_{X}, \sigma_{X}^{2}\right)\) and \(N\left(\mu_{Y}, \sigma_{Y}^{2}\right)\), respectively, and that \(\sigma_{Y}^{2}>\sigma_{X}^{2}\). Thus, use the modification of \(Z\) to test the hypothesis \(H_{0}: \mu_{X}-\mu_{Y}=0\) against the alternative hypothesis \(H_{1}: \mu_{X}-\mu_{Y}<0\).

(a) Define the test statistic and a critical region that has a significance level of \(\alpha=0.025\).

(b) Using the data given in Exercise 7.2-5, calculate the value of the test statistic and state your conclusion.

(c) Draw two box-and-whisker diagrams on the same figure. Does your figure confirm the conclusion of this exercise?

Equation Transcription:

 

 

 

 

 


Text Transcription:

X  

Y  

N(mu_X, sigma_X^2)  

N(mu_Y, sigma_Y^2)

sigma_Y^2>sigma_X^2  

Z  

H_0:mu_X-mu_Y=0  

H_1:mu_X-m_Y<0  

alpha=0.025

ANSWER:

Step 1 of 3

Null hypothesis:

Alternative hypothesis:

Given data

For X

For Y

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back