Suppose the covariance between Y and X is 10, the variance of Y is 25, and the variance of X is 64. The sample size is 30. Using a 5% level of significance, which of the following statements is most accurate? The null hypothesis of:
A) |
no correlation is rejected. | |
B) |
significant correlation is rejected. | |
C) |
no correlation cannot be rejected. | |
The correlation coefficient is r = 10 / (5 × 8) = 0.25. The test statistic is t = (0.25 × √28) / √(1 ? 0.0625) = 1.3663. The critical t-values are ± 2.048. Therefore, we cannot reject the null hypothesis of no correlation. |