A hypothesis test that a rank correlation coefficient is zero is conducted at the 5% level of significance. If the correlation coefficient is 0.50 for a sample of 15 observations, what is the computed value of the t statistic?
A) 0.456
B) 6.08
C) 2.2082
D) 2.2361

Question

Quizplus · Accepted Answer

The rank correlation coefficient is denoted by the symbol rho (ρ) and its null hypothesis is that it is equal to zero. The formula for the t-statistic in a hypothesis test for rank correlation coefficient is given by:
t = ρ * sqrt((n-2)/(1-ρ^2))
Substituting the values given in the question, we get:
t = 0.5 * sqrt((15-2)/(1-0.5^2)) = 2.2082
Therefore, the correct answer is C) 2.2082.

A Hypothesis Test That a Rank Correlation Coefficient Is Zero