When testing $$H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \leq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } 0$$ , the observed value of the Z test statistic was found to be - 2.13. The p-value for this test is
A) 0.0166.
B) 0.0332.
C) 0.9668.
D) 0.9834.

Question

When testing $$H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \leq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } > 0$$ , the observed value of the Z test statistic was found to be - 2.13. The p-value for this test is
A) 0.0166.
B) 0.0332.
C) 0.9668.
D) 0.9834.

Quizplus · Accepted Answer

The p-value for a one-tailed test with a Z statistic of -2.13 is the probability of observing a value less than -2.13, which is 0.0166. However, since the test is for $\pi_1 - \pi_2 > 0$, we need the probability of observing a value greater than 2.13, which is 1 - 0.0166 = 0.9834.

When Testing H0:π1−π2≤0 versus H1:π1−π2>0H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \leq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } > 0H0​:π1​−π2​≤0 versus H1​:π1​−π2​>0

When Testing $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \leq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } > 0$