Test the claim that the proportion of people who own cats is larger than $20 \%$ at the 0.10 significance level.
The null and alternative hypothesis would be:
\[
\begin{array}{cccccc}
H_{0}: \mu \geq 0.2 & H_{0}: \mu=0.2 & H_{0}: \mu \leq 0.2 & H_{0}: p \geq 0.2 & H_{0}: p=0.2 & H_{0}: p \leq 0.2 \\
H_{1}: \mu< 0.2 & H_{1}: \mu \neq 0.2 & H_{1}: \mu> 0.2 & H_{1}: p< 0.2 & H_{1}: p \neq 0.2 & H_{1}: p> 0.2 \\
\end{array}
\]
The test is:
two-tailed right-tailed left-tailed $0^{s}$
Based on a sample of 300 people, $25 \%$ owned cats
The $p$-value is:
(to 2 decimals)

Step 1 ：Define the null and alternative hypothesis. The null hypothesis is that the proportion of people who own cats is equal to 20%, and the alternative hypothesis is that the proportion of people who own cats is greater than 20%. This is a right-tailed test.

Step 2 ：We are given a sample of 300 people, and 25% of them own cats. Use this information to calculate the test statistic and the p-value.

Step 3 ：The test statistic is calculated as the difference between the sample proportion and the hypothesized proportion, divided by the standard error of the proportion. The standard error of the proportion is calculated as the square root of the product of the hypothesized proportion and its complement, divided by the sample size.

Step 4 ：The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed test statistic, under the null hypothesis. It is calculated using the standard normal distribution, because the test statistic follows a standard normal distribution under the null hypothesis.

Step 5 ：If the p-value is less than the significance level, we reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.

Step 6 ：Calculate the test statistic and the p-value. The test statistic is approximately 2.165 and the p-value is approximately 0.015.

Step 7 ：The p-value is less than the significance level of 0.10. Therefore, we reject the null hypothesis. This means that we have enough evidence to support the claim that the proportion of people who own cats is larger than 20% at the 0.10 significance level.

Step 8 ：Final Answer: The p-value is approximately \(\boxed{0.015}\). Therefore, we reject the null hypothesis. This means that we have enough evidence to support the claim that the proportion of people who own cats is larger than 20% at the 0.10 significance level.