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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 the propol who own cats. Assume the null hypothesis is that the population proportions are equal.
You sample 180 men, and \( 90 \% \) own cats.
You sample 100 women, and \( 25 \% \) own cats.
Find the test statistic, rounded to two decimal places.
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\(z = \frac{(p_1 - p_2) - 0}{\sqrt{\frac{(p_1 + p_2)(1 - (p_1 + p_2))}{180+100}}} = 6.08\)

Steps

Step 1 ：\(p_1 = \frac{90}{180} = 0.5\)

Step 2 ：\(p_2 = \frac{25}{100} = 0.25\)

Step 3 ：\(z = \frac{(p_1 - p_2) - 0}{\sqrt{\frac{(p_1 + p_2)(1 - (p_1 + p_2))}{180+100}}} = 6.08\)