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)2.082
D)2.2361

Question

Quizplus · Accepted Answer

A rank correlation coefficient is tested using a Spearman's rank correlation test, which uses a t-distribution. The t-statistic for this test is calculated by dividing the rank correlation coefficient by its standard error. The formula for standard error is SE = sqrt((1-r^2)/(n-2)). Plugging in the values given, we get SE = sqrt((1-0.5^2)/(15-2)) = 0.2259. The t-statistic is then calculated as (r-0)/SE = (0.5-0)/0.2259 = 2.21, which is closest to answer choice C (2.082).

A Hypothesis Test That a Rank Correlation Coefficient Is Zero