llabus
You are testing the claim that the proportion of men who own cats is larger than the proportion of women who own cats.
You sample 80 men, and $50 \%$ own cats.
You sample 160 women, and $45 \%$ own cats.
Find the test statistic, rounded to two decimal places.
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Step 1 ：Given that we have sampled 80 men and found that 50% of them own cats, we can calculate the number of men who own cats as \(n1 = 80\) and \(p1 = 0.5\), so \(x1 = n1 \times p1 = 40\).

Step 2 ：Similarly, we have sampled 160 women and found that 45% of them own cats, so we can calculate the number of women who own cats as \(n2 = 160\) and \(p2 = 0.45\), so \(x2 = n2 \times p2 = 72\).

Step 3 ：We can then calculate the pooled proportion \(p\) as \((x1 + x2) / (n1 + n2) = (40 + 72) / (80 + 160) = 0.467\).

Step 4 ：Finally, we can calculate the test statistic \(Z\) using the formula \(Z = (p1 - p2) / \sqrt{ (p(1-p)(1/n1 + 1/n2)) }\), which gives us \(Z = (0.5 - 0.45) / \sqrt{ (0.467(1-0.467)(1/80 + 1/160)) } = 0.73\).

Step 5 ：So, the test statistic, rounded to two decimal places, is \(\boxed{0.73}\).