Let X and Y denote the heights of blue spruce trees,

Chapter 8, Problem 10E

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Let \(X\) and \(Y\) denote the heights of blue spruce trees, measured in centimeters, growing in two large fields. We shall compare these heights by measuring 12 trees selected at random from each of the fields. Take \(\alpha \approx 0.05\), and use the statistic \(W-\) the sum of the ranks of the observations of \(Y\) in the combined sample - to test the hypothesis \(H_{0}: m_{X}=m_{Y}\) against the alternative hypothesis \(H_{1}: m_{X}<m_{Y}\) on the basis of the following \(n_{1}=12\) observations of \(X\) and \(n_{2}=12\) observations of \(Y\).

Equation Transcription:

 

Text Transcription:

X  

Y  

Alpha approx 0.05  

W

H_0: m_X=m_Y

H_1: m_X<m_Y

n_1=12

n_2=12