In testing $H _ { 0 } : p _ { 1 } - p _ { 2 } = 0 \text { versus } H _ { 0 } : p _ { 1 } - p _ { 2 } 0 \text {, where } p _ { 1 } \text { and } p _ { 2 }$ denote the two population proportions, and both sample sizes are assumed to be large, the rejection region for approximate level .025 test is
A) $z \leq - 1.96$
B) $z \geq 1.96$
C) either $z \leq - 1.96 \text { or } z \geq 1.96$
D) $z \leq - 1.65$
E) $z \geq 1.65$

Question

In testing $H _ { 0 } : p _ { 1 } - p _ { 2 } = 0 \text { versus } H _ { 0  } : p _ { 1 } - p _ { 2 } > 0 \text {, where } p _ { 1 } \text { and } p _ { 2 }$ denote the two population proportions, and both sample sizes are assumed to be large, the rejection region for approximate level .025 test is
A) $z \leq - 1.96$
B) $z \geq 1.96$
C) either $z \leq - 1.96 \text { or } z \geq 1.96$
D) $z \leq - 1.65$
E) $z \geq 1.65$

Quizplus · Accepted Answer

For a one-tailed test with an alpha level of .025, the critical z-value is 1.96. This corresponds to the area in the upper tail of the standard normal distribution. Since the alternative hypothesis suggests $p_1 - p_2 > 0$, we are interested in the right tail, making the rejection region $z \geq 1.96$.

In Testing H0:p1−p2=0 versus H0:p1−p2>0, where p1 and p2H _ { 0 } : p _ { 1 } - p _ { 2 } = 0 \text { versus } H _ { 0 } : p _ { 1 } - p _ { 2 } > 0 \text {, where } p _ { 1 } \text { and } p _ { 2 }H0​:p1​−p2​=0 versus H0​:p1​−p2​>0, where p1​ and p2​

In Testing $H _ { 0 } : p _ { 1 } - p _ { 2 } = 0 \text { versus } H _ { 0 } : p _ { 1 } - p _ { 2 } > 0 \text {, where } p _ { 1 } \text { and } p _ { 2 }$