Step 1 :1. \(p_{1} = 0.80\), \(n_{1} = 100\), \(p_{2} = 0.85\), \(n_{2} = 180\)
Step 2 :2. Compute pooled proportion: \(p = \dfrac{p_{1}n_{1} + p_{2}n_{2}}{n_{1} + n_{2}} = \dfrac{0.80(100) + 0.85(180)}{100+180} = \dfrac{80+153}{280} = \dfrac{233}{280}\)
Step 3 :3. Calculate test statistic: \(Z = \dfrac{(p_{1} - p_{2}) - 0}{\sqrt{\frac{p(1-p)}{n_{1}} + \frac{p(1-p)}{n_{2}}} } = \dfrac{(0.80-0.85) - 0}{\sqrt{\frac{\dfrac{233}{280}(1-\dfrac{233}{280})}{100} + \frac{\dfrac{233}{280}(1-\dfrac{233}{280})}{180}} } =\dfrac{-0.05}{\sqrt{\frac{233(47)}{280(100)} + \frac{233(47)}{280(180)}} } = -1.60\)