In the following, I understood that we fail to reject null hypothesis of correlation is 0. So, there may be not correlation. I thought significant is keyword and answer should contain it. What is wrong with it. 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 percent level of significance, which of the following statements is TRUE? The null hypothesis of: A) no correlation is rejected. B) significant correlation is rejected. C) significant correlation cannot be rejected. D) no correlation cannot be rejected. Your answer: B was incorrect. The correct answer was D) 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.

Just a semantics thing chinni. You could rearrange D to say significant correlation is not found. The null is no correlation and you Can’t reject it.

Test is: Null H(0): r = 0 (no correlation). Alternative H(1) r not = 0 (correlation). Decision is always to rehect null or not to reject null. In this case we can not reject null as 1.4 (actual) is less than 2.0 (critical). Therefore the observed correlation of 0.25 is not statistically significantly different from 0 at the 5% significance level and we conclude that no correlation can not be rejected.

got it. thanks to all