invic

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.

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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.

invic

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%, we:

A) conclude that there is significant correlation between X and Y.

B) conclude that there is no significant correlation between X and Y.

C) cannot test the significance of the correlation with this information.

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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.

invic

Consider a sample of 60 observations on variables X and Y in which the correlation is 0.42. If the level of significance is 5%, we:

A) cannot test the significance of the correlation with this information.

B) conclude that there is no significant correlation between X and Y.

C) conclude that there is statistically significant correlation between X and Y.

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The calculated t is t = (0.42 × √58) / √(1-0.42^2) = 3.5246 and the critical t is approximately 2.000. Therefore, we reject the null hypothesis of no correlation.

invic

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% level of significance, which of the following is most accurate? The null hypothesis of:

A) no correlation is rejected.

B) significant correlation is rejected.

C) no correlation is not rejected.

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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.

invic

A study of 40 men finds that their job satisfaction and marital satisfaction scores have a correlation coefficient of 0.52. At 5% level of significance, is the correlation coefficient significantly different from 0?

A) No, t = 1.68.

B) No, t = 2.02.

C) Yes, t = 3.76.

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H0: r = 0 vs. Ha: r ≠ 0
t = [r √(n – 2)] / √(1 – r2) <P >="[(0.52" √(38)] √(1 – 0.522)="3.76"
tc (α = 0.05 and degrees of freedom = 38) = 2.021
t > tc hence we reject H0.

invic

We are examining the relationship between the number of cold calls a broker makes and the number of accounts the firm as a whole opens. We have determined that the correlation coefficient is equal to 0.70, based on a sample of 16 observations. Is the relationship statistically significant at a 10% level of significance, why or why not? The relationship is:

A) significant; the t-statistic exceeds the critical value by 3.67.

B) not significant; the critical value exceeds the t-statistic by 1.91.

C) significant; the t-statistic exceeds the critical value by 1.91.

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The calculated test statistic is t-distributed with n – 2 degrees of freedom:
t = r√(n – 2) / √(1 – r2) = 2.6192 / 0.7141 = 3.6678
From a table, the critical value = 1.76

invic

One of the limitations of correlation analysis of two random variables is the presence of outliers, which can lead to which of the following erroneous assumptions?

A) The presence of a nonlinear relationship between the two variables, when in fact, there is a linear relationship.

B) The absence of a relationship between the two variables, when in fact, there is a linear relationship.

C) The presence of a nonlinear relationship between the two variables, when in fact, there is no relationship whatsoever between the two variables.

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Outliers represent a few extreme values for sample observations in a correlation analysis. They can either provide statistical evidence that a significant relationship exists, when there is none, or provide evidence that no relationship exists when one does.

invic

One major limitation of the correlation analysis of two random variables is when two variables are highly correlated, but no economic relationship exists. This condition most likely indicates the presence of:

A) outliers.

B) nonlinear relationships.

C) spurious correlation.

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Spurious correlation occurs when the analysis erroneously indicates a relationship between two variables when none exists.

invic

Ron James, CFA, computed the correlation coefficient for historical oil prices and the occurrence of a leap year and has identified a statistically significant relationship. Specifically, the price of oil declined every fourth calendar year, all other factors held constant. James has most likely identified which of the following conditions in correlation analysis?

A) Positive correlation.

B) Spurious correlation.

C) Outliers.

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Spurious correlation occurs when the analysis erroneously indicates a linear relationship between two variables when none exists. There is no economic explanation for this relationship; therefore this would be classified as spurious correlation.

invic

Suppose the covariance between Y and X is 12, the variance of Y is 25, and the variance of X is 36. What is the correlation coefficient (r), between Y and X?

A) 0.400.

B) 0.160.

C) 0.013.

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The correlation coefficient is: