Given the linear correlation coefficient r and the sample size n, determine the

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. Round to three decimal places.

r= -0.39 ; n=25

A. Critical values: r=±0.487,significant linear correlation

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

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

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

Explanation / 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.

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.


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

The value of r given in the problem statement (r = 0.39) is greater than 0.396. This shows there is a significant linear correlation.

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