Which of the Following Statements Are Not True?
A) the Correlation

Multiple Choice

Which of the following statements are not true?

A) The correlation coefficient r is a measure of how strongly related x and y are in the observed sample, while the correlation coefficient $\rho$
Is a measure of how strongly related x and y are in the population
B) When $\left( X _ { 1 } , Y _ { 1 } \right) , \left( X _ { 2 } , Y _ { 2 } \right) , \ldots \ldots \left( X _ { n } , Y _ { n } \right)$
Is a sample from a bivariate normal distribution, where $\mu _ { 1 } \text { and } \sigma _ { 1 }$
Are the mean and standard deviation of X, and $\mu _ { 2 } \text { and } \sigma _ { 2 }$
Are the mean and standard deviation of Y , then the random variable $V = \frac { 1 } { 2 } \ln \left( \frac { 1 + R } { 1 - R } \right)$
Where $R = \hat { \rho }$
Has approximately a t distribution with 2n degrees of freedom.
C) When $H _ { 0 } : \rho = 0$
Is true, the test statistic $T = R \sqrt { n - 2 } / \sqrt { 1 - R ^ { 2 } }$
Where $R = \hat { \rho } ,$
Has a t distribution with n -2 degrees of freedom.
D) All of the above statements are true
E) None of the above statements are true.