Use the one-proportion z-test to perform the specified hypothesis test. Use the critical-value approach.
-$\mathrm { x } = 18 , \mathrm { n } = 100 , \mathrm { H } _ { 0 } : \mathrm { p } = 0.2 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.2 , \alpha = 0.01$
A)$\mathrm { z } = - 0.500$; critical values $= \pm 2.575$; do not reject $\mathrm { H } _ { 0 }$
B) $\mathrm { z } = - 0.500$; critical values $= \pm 2.33$; do not reject $\mathrm { H } _ { 0 }$
C) $\mathrm { z } = - 0.310$; critical values $= \pm 2.575$; do not reject $\mathrm { H } _ { 0 }$
D) $\mathrm { z } = - 0.310$; critical values $= \pm 2.33$; reject $\mathrm { H } _ { 0 }$

Question

Use the one-proportion z-test to perform the specified hypothesis test. Use the critical-value approach.
-$\mathrm { x } = 18 , \mathrm { n } = 100 , \mathrm { H } _ { 0 } : \mathrm { p } = 0.2 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.2 , \alpha = 0.01$  
A)$\mathrm { z } = - 0.500$; critical values $= \pm 2.575$; do not reject $\mathrm { H } _ { 0 }$
B) $\mathrm { z } = - 0.500$; critical values $= \pm 2.33$; do not reject $\mathrm { H } _ { 0 }$
C) $\mathrm { z } = - 0.310$; critical values $= \pm 2.575$; do not reject $\mathrm { H } _ { 0 }$
D) $\mathrm { z } = - 0.310$; critical values $= \pm 2.33$; reject $\mathrm { H } _ { 0 }$

Quizplus · Accepted Answer

The correct z-value and critical values are needed to determine whether to reject $H_0$. The z-value is calculated using the formula for the one-proportion z-test. Given $\alpha = 0.01$ for a two-tailed test, the critical z-values are $\pm 2.575$. Since the calculated z-value does not exceed the critical values, we do not reject $H_0$.

Use the One-Proportion Z-Test to Perform the Specified Hypothesis Test