The explanation here does not match to the answer chosen A. Could you please explain what is happening in this problem. Appreciate for your time. --------------------------------- Consider a sample of 32 observations on variables X and Y in which the correlation is 0.30. If the level of significance is 5 percent, we: A) conclude that there is no significant correlation between X and Y. B) conclude that there is significant correlation between X and Y. C) conclude that there is little correlation between X and Y. D) cannot test the significance of the correlation with this information. Your answer: B was incorrect. The correct answer was A) conclude that there is no significant correlation between X and Y. The calculated t = (0.30*√30)/√(1-0.09) = 1.72251 and the critical t values are ± 2.042. Therefore, we fail to reject the null hypothesis of no correlation.
you test for null: rho=0 alternative: rho not equal to 0 you calculate the test static – in this case 1.72, however it is not above/below 2.042 meaning that you fail to reject the null. if you fail to reject the null - you have to “accept” it - thus result: rho=0 and no correlation between x and y.
here you go for another example http://www.analystforum.com/phorums/read.php?11,626990,626990#msg-626990