If a sample of 25 observations is selected, and the sample correlation coefficient between the variables x and y is r = 0.525, what is the test statistic value for testing
A) About 3.65.
B) About 2.96.
C) About 3.08.
D) About 3.81.
E) About 3.96.

Question

If a sample of 25 observations is selected, and the sample correlation coefficient between the variables x and y is r = 0.525, what is the test statistic value for testing 
A) About 3.65. 
B) About 2.96. 
C) About 3.08. 
D) About 3.81. 
E) About 3.96.

Quizplus · Accepted Answer

To test the hypothesis that the true correlation coefficient (ρ) equals zero, we use the test statistic t = r*(sqrt(n-2))/sqrt(1-r^2), where n is the sample size. 
Substituting the given values, we have t = 0.525*(sqrt(25-2))/sqrt(1-0.525^2) ≈ 2.96. 
Therefore, the best choice is B, which approximates the calculated test statistic value.

If a Sample of 25 Observations Is Selected, and the Sample