Evaluate the following formula for $p_{1}-p_{2}=\bar{p},=0.134106 \bar{q}=1-\bar{p}, x_{1}=62 x_{2}=19 n_{1}=297 n_{2}=307 \hat{p}_{1}=\frac{x_{1}}{n_{1}}$ and $\hat{p}_{2}=\frac{x_{2}}{n_{2}}$.
\[
z=\frac{\left(\hat{p}_{1}-\hat{p}_{2}\right)-\left(p_{1}-p_{2}\right)}{\sqrt{\frac{\bar{p} \cdot \bar{q}}{n_{1}}+\frac{\bar{p} \cdot \bar{q}}{n_{2}}}}
\]
$z=\square$ (Round to two decimal places as needed.)
Answer
\( z = \boxed{0.46} \)
Step 1 ：Calculate \( \hat{p}_{1} \) using the formula \( \hat{p}_{1} = \frac{x_{1}}{n_{1}} \)
Step 2 ：Calculate \( \hat{p}_{2} \) using the formula \( \hat{p}_{2} = \frac{x_{2}}{n_{2}} \)
Step 3 ：Calculate \( \bar{q} \) using the formula \( \bar{q} = 1 - \bar{p} \)
Step 4 ：Plug the values of \( \hat{p}_{1} \), \( \hat{p}_{2} \), \( \bar{p} \), and \( \bar{q} \) into the formula for \( z \)
Step 5 ：Calculate \( z \) and round to two decimal places
Step 6 ：\( z = \boxed{0.46} \)
