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 ${\hat{p}}_{2} = \frac{x_{2}}{n_{2}}$ .
$z = \frac{({\hat{p}}_{1} - {\hat{p}}_{2}) - (p_{1} - p_{2})}{\sqrt{\frac{\bar{p} \cdot \bar{q}}{n_{1}} + \frac{\bar{p} \cdot \bar{q}}{n_{2}}}}$
$z = ◻$ (Round to two decimal places as needed.)

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Answer

$z = 0.46$

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 ： $z = 0.46$