Question

A researcher computes r = 0.45 using a sample of 18 participants. Is this Pearson correlation coefficient significant for a two-tailed test at a .05 level of significance?

Answer 1

Answer with explanation:

Given : The computed r -value = 0.45

Sample size : n=18

Degree of freedom : $df=n-2=18-2=16$

Now, the critical value for Pearson correlation coefficient  for a two-tailed test at a .05 level of significance will be :

$r_c=0.468$   ( by critical correlation coefficient table)

Since , $r>r_c$ i.e. 0.45>0.468 , then we say that his Pearson correlation coefficient is not significant for a two-tailed test at a .05 level of significance.