The test is: right-tailed left-tailed two-tailed \( \sigma^{8} \) Based on a sample of 40 men, \( 45 \% \) owned cats Based on a sample of 40 women, \( 65 \% \) owned cats The test statistic is: (to 2 decimals) The \( \mathrm{p} \)-value is: Enter an integer or decimal number [more..] Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

Step 1 ：Find proportions: \(p_{men} = 0.45\), \(p_{women} = 0.65\)

Step 2 ：Compute difference in proportions: \(p_{difference} = p_{men} - p_{women} = 0.45 - 0.65 = -0.2\)

Step 3 ：Calculate standard error: \(SE = \sqrt{\frac{p_{men}(1-p_{men})}{n_{men}} + \frac{p_{women}(1-p_{women})}{n_{women}}} = \sqrt{\frac{0.45(1-0.45)}{40} + \frac{0.65(1-0.65)}{40}} = \sqrt{\frac{0.2475}{40} + \frac{0.2275}{40}} = 0.0684\)

Step 4 ：Find test statistic (z-score): \(z = \frac{p_{difference}}{SE} = \frac{-0.2}{0.0684} = -2.92\)

Step 5 ：Find \(\mathrm{p}\)-value using a two-tailed test: \(\mathrm{p} = 2 * P(Z < -|z|) = 0.0036\)

Step 6 ：Analyze result: since \(\mathrm{p}\)-value (0.0036) is less than the significance level (0.05), reject the null hypothesis