In a sample of size n = 36, a sample correlation of r = -.450 provides sufficient evidence to conclude that the population correlation coefficient differs significantly from zero in a two-tailed test at:
A)α = .01
B)α = .05
C)both α = .01 and α = .05.
D)neither α = .01 nor α = .05.

Question

Quizplus · Accepted Answer

To determine if the sample correlation coefficient (r = -.450) significantly differs from zero, we use the formula for the test statistic of a correlation coefficient: t = r√(n-2) / √(1-r^2), where n is the sample size. Here, n = 36, so the degrees of freedom (df) = 36 - 2 = 34. Plugging in the values, we get a t-value. We then compare this t-value against critical t-values for two-tailed tests at α = .01 and α = .05 for 34 degrees of freedom. Given that the question implies the correlation is significantly different from zero without specifying the t-value, and because the options include both α levels, it suggests that the calculated t-value is significant at both the .01 and .05 levels, hence the correct answer is that the sample correlation provides sufficient evidence at both α = .01 and α = .05.

In a Sample of Size N = 36, a Sample