Solution Found!
(In some of the exercises that follow, we must
Chapter 8, Problem 12E(choose chapter or problem)
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