Questions: Test the claim that the proportion of people who own cats is significantly different than 10% at the 0.05 significance level. The null and alternative hypothesis would be: H0: p=0.1 H1: p ≠ 0.1 The test is: two-tailed Based on a sample of 800 people, 16% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis

Solution Steps

We are testing the claim that the proportion of people who own cats is significantly different from \(10\%\). The hypotheses are defined as follows:

\[ \begin{align_} H_0: p = 0.1 \quad & \text{(Null Hypothesis)} \\ H_1: p \neq 0.1 \quad & \text{(Alternative Hypothesis)} \end{align_} \]

The test statistic for the proportion is calculated using the formula:

\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]

Substituting the values:

\[ Z = \frac{0.16 - 0.1}{\sqrt{\frac{0.1(1 - 0.1)}{800}}} = 5.66 \]

The P-value associated with the test statistic \(Z = 5.66\) is calculated to be:

\[ \text{P-value} = 0.0 \]

We compare the P-value to the significance level \(\alpha = 0.05\):

• If \(\text{P-value} < \alpha\), we reject the null hypothesis.
• If \(\text{P-value} \geq \alpha\), we fail to reject the null hypothesis.

Since \(0.0 < 0.05\), we reject the null hypothesis.

Final Answer