For a given set of twelve ranked data values, the sum of the squared differences is 63.18. What is the test statistic value to test the hypothesis that the rank correlation coefficient is zero?
A) -2.228
B) 2.228
C) 3.948
D) -3.948

Question

Quizplus · Accepted Answer

The test statistic for testing the hypothesis that the rank correlation coefficient is zero is given by:
t = rho * sqrt[(n-2)/(1-rho^2)]
where rho is the rank correlation coefficient and n is the number of observations.
Here, we are given the sum of squared differences as 63.18, which can be used to calculate the rank correlation coefficient as:
rho = 1 - (6*63.18)/(12*(12^2 - 1)) = -0.42
Substituting in the formula for the test statistic, we get:
t = -0.42 * sqrt[(12-2)/(1-(-0.42)^2)] = -3.948
Therefore, the best choice is C.

For a Given Set of Twelve Ranked Data Values, the Sum