(Solved): A veterinarian is interested in researching the proportion of men and women cat owners and believe ...

A veterinarian is interested in researching the proportion of men and women cat owners and believes that the proportion of men cat owners is significantly different than the proportion of women cat owners. The veterinarian decides to obtain two independent samples of men and women cat owners and finds from one sample of 80 men, \( 40 \% \) owned cats. In the second sample of 80 women, \( 60 \% \) owned cats. Test the veterinarian's belief at the \( \alpha=0.05 \) significance level. Preliminary: a. Is it safe to assume that \( n_{\text {men }} \leq 5 \% \) of all men and \( n_{\text {women }} \leq 5 \% \) of all women? Yes No b. Verify \( n \hat{p}(1-\hat{p}) \geq 10 \). Round your answer to one decimal place. \[ \begin{array}{ll} n_{\text {men }} \hat{p}(1-\hat{p})= & \sigma^{\infty} \\ n_{\text {women }} \hat{p}(1-\hat{p})= & \sigma^{\circ} \end{array} \] Test the claim: a. Determine the null and alternative hypotheses. \( \begin{array}{ll}H_{0}: p_{\text {men }} & p_{\text {women }} \\ H_{a}: p_{\text {men }} & p_{\text {women }}\end{array} \) b. The hypothesis test is two-tailed left-tailed right-tailed c. Determine the test statistic. Round to two decimal places. \[ z= \] \( \sigma^{\circ} \) d. Find the \( p \)-value. Round to four decimal places. \[ p \text {-value }= \] \( \sigma^{8} \) e. Make a decision. Fail to reject the null hypothesis. Reject the null hypothesis. f. Write the conclusion. There is enough evidence to support the veterinarian's belief. There is not enough evidence to support the veterinarian's belief.