Reading 11- LOS C : Q2 following, hypothesis, class, between, statements

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2.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 most accurate? The null hypothesis of:

A)   no correlation is rejected.

B)   significant correlation is rejected.

C)   no correlation cannot be rejected.

D)   significant correlation cannot be rejected.

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The correct answer was C)

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.