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Computing the Standardize Test Statistic
You are testing the claim that the proportion of men who own cats is larger than th who own cats. Assume the null hypothesis is that the population proportions are eq
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.
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Answer

$z \approx - 20.58$

Steps

Step 1 ： $p_{m} = \frac{0.10}{1}$

Step 2 ： $p_{w} = \frac{0.60}{1}$

Step 3 ： $n_{m} = 180, n_{w} = 60$

Step 4 ： $p_{c} = \frac{0.10 * 180 + 0.60 * 60}{180 + 60}$

Step 5 ： $q_{c} = 1 - p_{c}$

Step 6 ： $z = \frac{(p_{m} - p_{w}) - 0}{\sqrt{\frac{p_{c} * q_{c}}{n_{m}} + \frac{p_{c} * q_{c}}{n_{w}}}}$

Step 7 ： $z \approx - 20.58$