A hypothesis test is conducted at the 5 percent level of significance to test whether the population correlation is zero.If the sample consists of 25 observations and the correlation coefficient is .60,what is the computed test statistic?
A)2.071
B)1.960
C)3.597
D)1.645

Question

Quizplus · Accepted Answer

The test statistic for testing the correlation coefficient is given by:
t = r (n - 2) / √(1 - r²)
where r is the sample correlation coefficient and n is the sample size.
Substituting the given values, we get:
t = 0.60 * (25 - 2) / √(1 - 0.60²) ≈ 3.597
Using a t-distribution with 23 degrees of freedom (n - 2), and a significance level of 0.05, the critical value is approximately 2.069. Since the computed test statistic (3.597) is greater than the critical value (2.069), we reject the null hypothesis and conclude that there is a significant correlation between the two variables. Therefore, the best choice is C.

A Hypothesis Test Is Conducted at the 5 Percent Level