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 : $\rho$ = 0 against the one-sided alternative H1 : $\rho$ $\lt$ 0 .To testH0 : $\rho$=0 against the two-sided alternative H1 : $\rho$$\neq$ 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)

Question

Quizplus · Accepted Answer

For a two-sided test, the p-value is doubled from the one-sided test if the original p-value is for the direction not included in the alternative hypothesis. Since the original test was for a less than alternative and we are moving to a not equal alternative, we double the original p-value. However, the correct mathematical representation for doubling the p-value is not clearly presented due to formatting issues, but the conceptually correct approach is to take 2 times the original p-value, which is closest to option D given the formatting errors.

The Sample Correlation Coefficient Between X and Y Is 0 ρ\rhoρ

The Sample Correlation Coefficient Between X and Y Is 0 $\rho$