If $n=320$ and $\hat{p}$ ( $p$-hat) $=0.55$, construct a $99 \%$ confidence interval.
Give your answers to three decimals
\[
< p<
\]

Step 1 ：We are given that the sample size, \(n\), is 320 and the sample proportion, \(\hat{p}\), is 0.55.

Step 2 ：We are asked to construct a 99% confidence interval for the proportion. The Z-score corresponding to a 99% confidence interval is approximately 2.576.

Step 3 ：The formula for a confidence interval for a proportion is given by \(\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\).

Step 4 ：Substituting the given values into the formula, we get \(0.55 \pm 2.576 \sqrt{\frac{0.55(1-0.55)}{320}}\).

Step 5 ：Solving the above expression, we get the lower and upper bounds of the confidence interval as 0.478 and 0.622 respectively.

Step 6 ：\(\boxed{0.478 < p < 0.622}\) is the 99% confidence interval for the proportion.