Final answer:
To determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size, calculate the degrees of freedom, look up the critical value in the table, and compare it to the correlation coefficient.
Step-by-step explanation:
To determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size, we can use the table of critical values for the correlation coefficient. First, we calculate the degrees of freedom, which is equal to n - 2. In this case, n is 27, so the degrees of freedom is 27 - 2 = 25.
Next, we look up the critical value in the table using the degrees of freedom and the level of significance (α = 0.05). The critical value is ±0.432.
Finally, we compare the correlation coefficient (r = -0.489) to the critical value. Since -0.489 is within the range of -0.432 to 0.432, it is not statistically significant at the α = 0.05 level. Therefore, we cannot conclude that there is a significant linear relationship.