Problem

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

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Answer

\( z = \boxed{0.46} \)

Steps

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 :\( z = \boxed{0.46} \)

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