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 0.1, 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 we test the one-sided alternative hypothesis, the p-value is only considered in one direction. To find the p-value for H₁: ρ < 0, we need to divide the two-sided p-value by 2.

Therefore, the p-value for H₁: ρ < 0 is 1 - 0.256/2 = 0.872.

Hence, the answer is D.

The Sample Correlation Coefficient Between X and Y Is 0