The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.744 when testing 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 0.744 when testing H₀: ρ = 0 against the one-sided alternative H₁: ρ < 0. To test H₀: ρ = 0 against the two-sided alternative H₁: ρ ≠ 0 at a significance level of 0.1, the p-value is
A) 0.744/2.
B) (0.744)(2).
C) 1 - 0.744.
D) (1 - 0.744)(2).

Quizplus · Accepted Answer

To test H₀: ρ = 0 against the two-sided alternative H₁: ρ ≠ 0, we need to divide the one-sided p-value by 2 since it is a two-tailed test. Therefore, the p-value is 0.744/2 = 0.372. However, this is still the p-value for H₁: ρ < 0 since we were given that alternative hypothesis. So, to find the p-value for H₁: ρ ≠ 0, we need to double the one-sided p-value, which gives (1 - 0.744) x 2 = 0.512. Since this p-value is greater than the significance level of 0.1, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a linear relationship between X and Y.

The Sample Correlation Coefficient Between X and Y Is 0