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 0.60, then the computed test statistic would be:
A)2.071.
B)1.960.
C)3.597.
D)1.645.

Question

Quizplus · Accepted Answer

The test statistic to test the null hypothesis of zero correlation coefficient is calculated using the formula:

t = r * √(n-2) / √(1-r^2)

where r is the sample correlation coefficient and n is the sample size.

Substituting the given values, we get:

t = 0.60 * √(25-2) / √(1-0.60^2) = 3.597

Using a t-table with 23 degrees of freedom (df = n-2), at a 5% significance level, the critical t-value is 2.069. Since our calculated t-value of 3.597 is greater than the critical t-value of 2.069, we reject the null hypothesis that the population correlation is zero. Therefore, the best choice is option C, 3.597.

A Hypothesis Test Is Conducted at the 5 Percent Level