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 = 0.543, n = 25

Answer 1

Answer:  r represents a significant linear correlation.

Step-by-step explanation:

GIven : Linear correlation coefficient: r = 0.543

Sample size: n= 25

Significance levle: $\alpha=0.05$

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

Now, we check r critical value table for value with df = 23 and $\alpha=0.05$.

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.

Answer 2

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 :

• Confidence level = 0.05
• Correlation Coefficient, r = 0.543
• Sample size, n = 25

Recall :

• Degree of freedom, df = n - 2 = 25 - 2 = 23

Decision Region :

• Reject H0 if r > Critical value

Critical value at T0.05, 23 = ±0.396

Comparing the critical value and correlation Coefficient :

• 0.543 > 0.396

Hence, the correlation Coefficient is significant.

Learn more : https://brainly.com/question/14454192