Use the one-proportion z-test to perform the specified hypothesis test. Use the critical-value approach.
-$\mathrm { x } = 30 , \mathrm { n } = 169 , \mathrm { H } _ { 0 } : \mathrm { p } = 0.11 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.11 , \alpha = 0.05$
A)$\mathrm { z } = 1.36$; critical values $= \pm 1.96$; do not reject $\mathrm { H } _ { 0 }$
B) $\mathrm { z } = 2.81$.; critical values $= \pm 1.645$; reject $\mathrm { H } _ { 0 }$
C) $\mathrm { z } = 1.36$.; critical values $= \pm 1.645$; do not reject $\mathrm { H } _ { 0 }$
D) $\mathrm { z } = 2.81$.; critical values $= \pm 1.96$; reject $\mathrm { H } _ { 0 }$

Question

Use the one-proportion z-test to perform the specified hypothesis test. Use the critical-value approach.
-$\mathrm { x } = 30 , \mathrm { n } = 169 , \mathrm { H } _ { 0 } : \mathrm { p } = 0.11 , \mathrm { H } _ { \mathrm { a } } : \mathrm { p } \neq 0.11 , \alpha = 0.05$  
A)$\mathrm { z } = 1.36$; critical values $= \pm 1.96$; do not reject $\mathrm { H } _ { 0 }$
B) $\mathrm { z } = 2.81$.; critical values $= \pm 1.645$; reject $\mathrm { H } _ { 0 }$
C) $\mathrm { z } = 1.36$.; critical values $= \pm 1.645$; do not reject $\mathrm { H } _ { 0 }$
D) $\mathrm { z } = 2.81$.; critical values $= \pm 1.96$; reject $\mathrm { H } _ { 0 }$

Quizplus · Accepted Answer

The correct z-score calculation for the given data ($x = 30, n = 169, p = 0.11$) results in a z-score of 2.81. Given the two-tailed test with $\alpha = 0.05$, the critical z-values are $\pm 1.96$. Since $2.81 > 1.96$, we reject $H_0$.

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