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 = 0.543, n = 25

Using the principle of hypothesis testing, the correlation Coefficient is greater than the critical value. Hence, the linear correlation Coefficient value is significant.

Given the Parameters :

Recall :

Decision Region :

Critical value at T0.05, 23 = ±0.396

Comparing the critical value and correlation Coefficient :

Hence, the correlation Coefficient is significant.

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 r represents a significant linear correlation.

Step-by-step explanation:

GIven : Linear correlation coefficient: r = 0.543

Sample size: n= 25

Significance levle:

Degree of freedom : n-2 = 25-2=23

Now, we check r critical value table for value with df = 23 and .

Critical value = ±0.396  [From r critical value table]

Since r = 0.543 > 0.396, that means there is significant linear correlation.

Hence,  r represents a significant linear correlation.

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