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

To test H₀: ρ = 0 against the one-sided alternative H₁: ρ < 0, the p-value can be calculated as the one-tailed p-value divided by 2. This is because the one-tailed p-value is the probability of obtaining a correlation coefficient as small or smaller than the calculated value when the true population correlation coefficient is 0. Thus, the p-value for this one-sided test is 0.256/2 = 0.128. 
Since we are testing at a significance level of 0.1, we reject the null hypothesis if the p-value is less than 0.1. Since the p-value of 0.128 is greater than 0.1, we fail to reject the null hypothesis. 
Therefore, the answer is D, 1-0.256/2 = 0.872.

The Sample Correlation Coefficient Between X and Y Is 0