sided-p-value-approximation-for-r-045-and-n-22-state-the-conclusion-at-alpha-005

Question

Using the relationship between correlation r and the t statistic for testing beta = 0 (t = r * $$sqrt((n-2)/(1-r^2$$))), compute the t statistic and two-sided p-value approximation for r = 0.45 and n = 22. State the conclusion at alpha = 0.05.

Accepted Answer

t ≈ 2.253, two-sided p ≈ 0.04; reject H0 and conclude evidence of linear association.

Answer

t ≈ 2.253, two-sided p ≈ 0.30; fail to reject H0 because p is larger than 0.05.

Answer

t ≈ 1.10, two-sided p ≈ 0.28; fail to reject H0 since correlation is weak and not significant.

Answer

t ≈ 3.50, two-sided p ≈ 0.001; reject H0 strongly due to large t value.

Using the relationship between correlation r and the t statistic for testing beta = 0 (t = r * sqrt((n-2)/(1-r^2))), compute the t statistic and two-sided p-value approximation for r = 0.45 and n = 22. State the conclusion at alpha = 0.05.