Explanation It is known that if two independent samples are moderately large, then the random variables, X i = ( 1 2 ) ln ( 1 + r i 1 − r i ) ~ N ( ( 1 2 ) ln ( 1 + ρ i 1 − ρ i ) , 1 n i − 3 ) , i = 1 , 2 , ... The random variables static and flow-through LC50 measurements have correlations r 1 and r 2 , each being computed from two independent samples of size n 1 and n 2 respectively. The null and alternative hypotheses are stated as follows: H 0 : ρ 1 = ρ 2 H a : ρ 1 ≠ ρ 2 The significance level is 0.05. It is given that, r 2 = 0.85 and n 2 = 20 . From Exercise 11.51, it is found that, r 1 = 0.959 , n 1 = 10 The test statistic is computed as follows: Z = ( 1 2 ) ln ( 1 + r 1 1 − r 1 ) − ( 1 2 ) ln ( 1 + r 2 1 − r 2 ) 1 n 1 − 3 + 1 n 2 − 3 = ( 1 2 ) ln ( 1 + 0

Mathematical Statistics with Applications

7th Edition

ISBN: 9780495110811

Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer

Publisher: Cengage Learning

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Chapter 11.8, Problem 60E

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Conduct a hypothesis test that the two correlation coefficients between static and flow-through LC50 measurements are equal.

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Chapter 11 Solutions

Mathematical Statistics with Applications

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Conduct a hypothesis test that the two correlation coefficients between static and flow-through LC50 measurements are equal.

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Conduct a hypothesis test that the two correlation coefficients between static and flow-through LC50 measurements are equal.

Chapter 11 Solutions