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 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 statistic is -2.13 and the test is one-tailed (right-tailed), we look for the probability of Z being greater than -2.13, which is equivalent to 1 minus the probability of Z being less than -2.13. This corresponds to choice D, 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 $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \leq 0 \text { versus } H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } > 0$