Answer: 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.