The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H₀ : ρ = 0 against the two-sided alternative H₁ : ρ ≠ 0. To test H₀ : ρ = 0 against the one-sided alternative H₁ : ρ

Question

The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H₀ : ρ = 0 against the two-sided alternative H₁ : ρ ≠ 0. To test H₀ : ρ = 0 against the one-sided alternative H₁ : ρ < 0 at a significance level of 0.2, the p-value is A) 0.256/2. B) (0.256)2 C) 1 - 0.256 D) 1 - 0.256/2

Quizplus · Accepted Answer

When testing a one-sided alternative at a significance level of 0.2, we need to compare the p-value to 0.2. Since the alternative is now one-sided, we only need to consider half of the p-value from the two-sided test. So, we divide 0.256 by 2 to get 0.128. Finally, we subtract this value from 1 to get the p-value for the one-sided test, which is 1 - 0.128 = 0.872. Therefore, the answer is D.

The Sample Correlation Coefficient Between X and Y Is 0