A survey asked, "How many tattoos do you currently have on your body?" Of the 1208 males surveyed, 186 responded that they had at least one tattoo. Of the 1096 females surveyed, 142 responded that they had at least one tattoo. Construct a 99% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval. What is the lower and upper bound ? (Round to three decimal places as needed.)

Step 1 ：Define the given values: \(n_1 = 1208\), \(n_2 = 1096\), \(\hat{p}_1 = \frac{186}{1208} = 0.154\), \(\hat{p}_2 = \frac{142}{1096} = 0.130\), and \(Z_{\alpha/2} = 2.576\) for a 99% confidence level.

Step 2 ：Calculate the standard error (SE) using the formula \(SE = \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\). Substituting the given values, we get \(SE = 0.015\).

Step 3 ：Calculate the confidence interval (CI) using the formula \(CI = \hat{p}_1 - \hat{p}_2 \pm Z_{\alpha/2} \times SE\). Substituting the given values, we get \(CI = 0.154 - 0.130 \pm 2.576 \times 0.015\).

Step 4 ：Solve the above equation to get the lower and upper bounds of the confidence interval. The lower bound is -0.013 and the upper bound is 0.062.

Step 5 ：Interpret the confidence interval: The 99% confidence interval for the difference between the proportion of males that have at least one tattoo and the proportion of females that have at least one tattoo is \([-0.013, 0.062]\). This means that we are 99% confident that the true difference in proportions lies within this interval. Since the interval contains 0, we cannot conclude that there is a significant difference between the proportions of males and females that have at least one tattoo.

Step 6 ：\(\boxed{\text{Final Answer: The lower bound is -0.013 and the upper bound is 0.062.}}\)