The table shows the number satisfied in their work in a sample of working adults with a college education and in a sample of working adults without a college education. Assume that you plan to use a significance level of $\alpha = 0.05 \text { to test the claim that } \mathrm { p } _ { 1 } \mathrm { p } _ { 2 }$ Find the critical value(s) for this hypothesis test. Do the data provide sufficient evidence that a greater proportion of those with a college education are satisfied in their work?
$\begin{array}{lcc}
\hline & \text { College Education } & \text { No College Education } \
\hline \text { Number in sample } & 194 & 188 \
\text { Number satisfied in their work } & 74 & 70 \
\hline
\end{array}$

A) $z = \pm 1.96$; no
B) $z = 1.96$; yes
C) $\mathrm { z } = 1.645$; no
D) $\mathrm { z } = - 1.645$; yes

Question

The table shows the number satisfied in their work in a sample of working adults with a college education and in a sample of working adults without a college education. Assume that you plan to use a significance level of $\alpha = 0.05 \text { to test the claim that } \mathrm { p } _ { 1 } > \mathrm { p } _ { 2 }$ Find the critical value(s) for this hypothesis test. Do the data provide sufficient evidence that a greater proportion of those with a college education are satisfied in their work? 
$\begin{array}{lcc}
\hline & \text { College Education } & \text { No College Education } \
\hline \text { Number in sample } & 194 & 188 \
\text { Number satisfied in their work } & 74 & 70 \
\hline
\end{array}$

A) $z = \pm 1.96$; no
B) $z = 1.96$; yes
C) $\mathrm { z } = 1.645$; no
D) $\mathrm { z } = - 1.645$; yes

Quizplus · Accepted Answer

The hypothesis test is one-tailed (right-tailed) since we are testing if $ p_1 > p_2 $. The critical value for a one-tailed test at $\alpha = 0.05$ is $z = 1.645$. The data does not provide sufficient evidence to support the claim, hence "no".

The Table Shows the Number Satisfied in Their Work in a Sample