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linear correlation coefficient r and the sample size n, Statistics










































Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

r = 0.399, n = 25

Critical values: r = ±0.487, no significant linear correlation
Critical values: r = ±0.396, no significant linear correlation
Critical values: r = ±0.396, significant linear correlation
Critical values: r = ±0.487, significant linear correlation

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Dec 17, 2011
CRITICAL CORRELATION COEFFICIENT
by: Staff

Question:

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

r = 0.399, n = 25

multiple choice:

A. Critical values: r = ±0.487, no significant linear correlation
B. Critical values: r = ±0.396, no significant linear correlation
C. Critical values: r = ±0.396, significant linear correlation
D. Critical values: r = ±0.487, significant linear correlation



Answer:

To answer this question, I used the Critical Values of the Pearson Product-Moment Correlation Coefficient table.

The level of significance for a two-tailed test is 0.05

The degrees of freedom = n - 2 = 25 - 2 = 23

(from the table) The critical value of the correlation coefficient is ±0.396.



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The answer to Part I of your question is:

± .396 is the CRITICAL CORRELATION COEFFICIENT for a level of significance of 0.05 for a sample of 25.

When the correlation coefficient (for a sample of 25 drawn from the same population) is equal to or above .396 (absolute value), there is a 95% chance that the relationship between the variables you observed in your original sample will exist.


C. Critical values: r = ±0.396, significant linear correlation



The answer to Part II of your question is:


The value of r given in the problem statement (r = 0.399) is greater than 0.396. This shows there is a significant linear correlation.







Thanks for writing.


Staff
www.solving-math-problems.com



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