Problem
Computing the Standardize Test Statistic You are testing the claim that the proportion of men who own ca who own cats. Assume the null hypothesis is that the population You sample 180 men, and \( 10 \% \) own cats. You sample 60 women, and \( 60 \% \) own cats. Find the test statistic, rounded to two decimal places.
Solution
Step 1 ：Step 1: Calculate \(p_1\), \(p_2\), \(n_1\), and \(n_2\). Set \(p_1 = 0.1\) and \(n_1 = 180\) for men, and \(p_2 = 0.6\) and \(n_2 = 60\) for women.
Step 2 ：Step 2: Calculate the pooled proportion \(\hat{p} = \frac{n_1 p_1 + n_2 p_2}{n_1+n_2}\), which is \(\hat{p} = \frac{180(0.1) + 60(0.6)}{180+60}\).
Step 3 ：Step 3: Calculate the test statistic \(Z = \frac{(p_1 - p_2) - 0}{\sqrt{\hat{p}(1 - \hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}}\) using the values from Steps 1 and 2.
