the proportion of people that own cats is 20\%. A veterinarian believes that this proportion is smaller than $20 \%$ and surveys 200 people. Test the veterinarian's claim at the $a=0.025$ significance level. Based on the sample of 200 people, $11 \%$ owned cats. Calculate the test statistic. Round to two decimal places.

Step 1 ：We are given that the proportion of people that own cats is 20\%. A veterinarian believes that this proportion is smaller than 20\% and surveys 200 people. The significance level is set at 0.025. Based on the sample of 200 people, 11\% owned cats. We are asked to calculate the test statistic.

Step 2 ：The test statistic for a proportion is calculated using the formula: \[Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\] where: \(\hat{p}\) is the sample proportion, \(p_0\) is the hypothesized population proportion, and \(n\) is the sample size.

Step 3 ：In this case, \(\hat{p} = 0.11\), \(p_0 = 0.20\), and \(n = 200\). We can substitute these values into the formula to calculate the test statistic.

Step 4 ：Substituting the given values into the formula, we get: \[Z = \frac{0.11 - 0.20}{\sqrt{\frac{0.20(1-0.20)}{200}}}\]

Step 5 ：Solving the above expression, we get the test statistic as -3.181980515339464

Step 6 ：Rounding to two decimal places, the test statistic is -3.18

Step 7 ：Final Answer: The test statistic is \(\boxed{-3.18}\)