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 significant level of 0.193,the p-value will be equal to A)0.128 B)0.512 C)0.744 D)0.872

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 significant level of 0.193,the p-value will be equal to A)0.128 B)0.512 C)0.744 D)0.872

Quizplus · Accepted Answer

Since we are testing for a one-sided alternative where $\rho > 0$, we only need to consider the right tail of the distribution. Using a table or calculator, we find that the area to the right of 0.375 (the sample correlation coefficient) under the null distribution (where $\rho = 0$) is 0.256. To find the p-value for the one-sided alternative, we need to double this value to account for both tails of the distribution, giving us a p-value of 0.512. Since this p-value is greater than the significance level of 0.193, we fail to reject the null hypothesis. Therefore, the best choice is (A) 0.128 as this is the one-tailed p-value for the null hypothesis (where $\rho = 0$) at the 0.193 significance level. This value is simply half of the two-tailed p-value calculated earlier.

The Sample Correlation Coefficient Between X and Y Is 0