  # 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

### Comments for linear correlation coefficient r and the sample size n, Statistics

 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 = 25multiple choice:A. Critical values: r = ±0.487, no significant linear correlationB. Critical values: r = ±0.396, no significant linear correlationC. Critical values: r = ±0.396, significant linear correlationD. Critical values: r = ±0.487, significant linear correlationAnswer: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 0.05The degrees of freedom = n - 2 = 25 - 2 = 23(from the table) The critical value of the correlation coefficient is ±0.396.Open the following link to view the table of values.(1) If your browser is Firefox, click the following link to VIEW; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter: Use the Backspace key to return to this page:http://www.solving-math-problems.com/images/Critical-Values-Correlation_Coefficient-2011-12-17.png 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 correlationThe 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