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=0.105, n=15

A: Critical values: r= +0.514, no significant linear correlations

B: Critical values: r= +0.514, significant linear correlation

C: Critical values: r= +0.532, no significant linear correlation

D: Critical values: r= 0.514, no significant linear correlation

WILL MARK BRAINLIEST !!!

A: Critical values: r= ±0.514, no significant linear correlations

Step-by-step explanation:

The correlation coefficient (r) = 0.105

Sample size (n)= 15

Significance level = 0.05

Using the Pearson Product-Moment Correlation Coefficient table:

degree of freedom (df) = n- 2

15 - 2 = 13

Looking up the table at 0.05 significance levels and a degree of freedom equals 13,

The critical value equals ±0.513977

If the correlation coefficient(0.105) obtained is greater or equal to the critical value (0.513977), then at the 0.05 significance level, a linear relationship exists between the observed variables.

However, the correlation coefficient (0.105) is less than the critical value (0.513977), therefore, no linear relationship exist.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,