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=0.767, n=25 A. Critical values: r= +0.396, no significant linear correlation B. Critical values: r= +0.487, no significant linear correlation C. Critical values: r = +0.396, significant linear correlation D. Critical values: r = + 0.487, significant linear correlation

Answer 1

Answer:

C. Critical values: r = +0.396

Step-by-step explanation:

Hello!

A linear correlation for two variables X₁ and X₂ was calculated.

For a sample n= 25 the sample correlation coefficient is r= 0.767.

Be the hypotheses:

H₀: ρ = 0

H₁: ρ ≠ 0

α: 0.05

For this hypothesis test, the rejection region is two-tailed, and the degrees of freedom are Df= n-2= 25-2= 23

So using the Pearson product-moment correlation coefficient table of critical values, under the entry for "two tailed tests" you have to cross the level of significance and the degrees of freedom to find the corresponding critical value:

$r_{n-2;\alpha }= r_{23;0.05}= 0.396$

Since the calculated correlation coefficient is greater than the critical value, you can reject the null hypothesis, this means that the correlation is significant at level 5%

I hope this helps!