Final answer:
The correlation of r = 0.60 in a sample size of n = 10 participants is tested for significance using a two-tailed test with α = 0.05. If the p-value is less than 0.05 or the computed r exceeds the critical values from the relevant table, the null hypothesis is rejected, indicating a significant correlation.
Step-by-step explanation:
To determine whether the correlation of r = 0.60 for a sample size of n = 10 participants is significant, one can perform a hypothesis test using a two-tailed test at the alpha level (α) of 0.05. The null hypothesis (H0) in this context would posit that there is no correlation in the population (ρ = 0), while the alternative hypothesis (H1) would suggest that there is a significant correlation.
To conduct the test, the sample correlation coefficient (r), the sample size (n), and the alpha level (α) are used. Since the degrees of freedom (df) for this test is n - 2 (which equals 8 for this example), we would refer to a table of critical values or use software to obtain the p-value.
For instance, if we find that the p-value is less than the significance level (α = 0.05), we would reject the null hypothesis, concluding there is sufficient evidence of a significant linear relationship between the two variables in the population. In contrast, if the p-value is greater than the significance level, we fail to reject the null hypothesis, implying the evidence does not support a significant correlation.
For this specific instance, if the p-value is indeed 0.026, which is less than the significance level of 0.05, the decision would be to reject H0, concluding that there is a significant correlation. Similarly, using a table of critical values with 8 degrees of freedom for α = 0.05, if the computed r value exceeds the positive and negative critical values, it indicates a significant correlation.