When testing $$H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \geq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 }

Question

When testing $$H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \geq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } < 0$$ , 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 found by looking at the standard normal distribution. The p-value is the probability of observing a value as extreme as -2.13 or more extreme in the negative direction, which is 0.0166.

When Testing H0:π1−π2≥0 versus H1:π1−π2<0H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \geq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } < 0H0​:π1​−π2​≥0 versus H1​:π1​−π2​<0

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