Week 8 Homework
Score: \( 12.2 / 44 \quad 5 / 14 \) answered
Question 9
Computing the Standardize Test Statistic
You are testing the claim that the proportion of men who own cats is smaller than the pro who own cats. Assume the null hypothesis is that the population proportions are equal.
You sample 140 men, and \( 35 \% \) own cats.
You sample 180 women, and \( 90 \% \) own cats.
Find the test statistic, rounded to two decimal places.
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Answer

Step 3: Find the test statistic: \( Z = \frac{\hat{p}_1 - \hat{p}_2}{SE} \)

Steps

Step 1 ：Step 1: Calculate the pooled proportion: \( p \) = \( \frac{x_1 + x_2}{n_1 + n_2} \)

Step 2 ：Step 2: Compute the standard error: \( SE = \sqrt{\frac{p(1 - p)}{n_1} + \frac{p(1 - p)}{n_2}} \)

Step 3 ：Step 3: Find the test statistic: \( Z = \frac{\hat{p}_1 - \hat{p}_2}{SE} \)