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 is the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. Since the test is left-tailed (due to the "<" in the alternative hypothesis), the p-value is found by looking up the Z score of -2.13 in the standard normal distribution table, which gives a p-value of approximately 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 $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \geq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } < 0$