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

question 22

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.

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