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 H ₀: r = 0 against the two-sided alternative H ₁: r ¹ 0. To test H ₀: r = 0 against the one-sided alternative H ₁: r 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 H ₀: r = 0 against the two-sided alternative H ₁: r ¹ 0. To test H ₀: r = 0 against the one-sided alternative H ₁: r > 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

For a one-sided test, the p-value is half of the two-sided test if the direction of the test (positive correlation in this case) matches the sign of the sample correlation coefficient. Since the original two-sided p-value is 0.256, halving it gives 0.128, which is appropriate for a one-sided test with r > 0.

The Sample Correlation Coefficient Between X and Y Is 0