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 0.2, 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 the two-sided alternative, we need to calculate the p-value for H₁ : ρ ≠ 0. Since the alternative hypothesis is two-sided, we need to divide the one-sided p-value (0.744) by 2 to get the correct p-value for the two-sided test. Thus, the p-value for H₁ : ρ ≠ 0 is 0.744/2 = 0.372. Since the significance level is 0.2, we reject the null hypothesis if the p-value is less than 0.2. Since p-value (0.372) is greater than 0.2, we fail to reject the null hypothesis. Therefore, the correct answer is D, (1 - 0.744)(2).

The Sample Correlation Coefficient Between X and Y Is 0