Question

Determine whether the correlation coefficient is statistically significant at the specified

level of significance for the given sample size.

r = 0.403, ? = 0.05, n = 25

Answer 1

To determine the significance of the correlation coefficient at 0.05 level of significance we can use the P-value method or the critical value approach. Here we will use the critical value approach.

To test the significance following hypothesis is conducted as:

Where ρ is population correlation

Rejection region:

Reject Ho if ∣r∣>rc​=0.396, where rc is computed at the degree of freedom df = n-2 and the level of significance 0.05 using the table shown below.

Conclusion:

Since the r which is given as 0.403 is greater than 0.396 hence we can reject the null hypothesis and conclude that at 0.05 level of significance the correlation coefficient is statistically significant.

Table:

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