Reading 11- LOS C : Q5 style

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5.Suppose the covariance between Y and X is 0.03 and that the variance of Y is 0.04 and the variance of X is 0.12. The sample size is 30. Using a 5 percent level of significance, which of the following is most accurate? The null hypothesis of:

A)   no correlation is not rejected.

B)   no correlation is rejected.

C)   significant correlation is rejected.

D)   significant correlation cannot be rejected.

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The correct answer was B)

The correlation coefficient is r = 0.03/(√0.04*√0.12) = 0.03/(0.2000*0.3464) = 0.4330.

The test statistic is t = (0.4330*√28)/√(1-0.1875) = 2.2912/0.9014 = 2.54.

The critical t-values are ± 2.048. Therefore, we reject the null hypothesis of no correlation.