Several years ago, $34 \%$ of parents who had children in grades K-12 were satisfied with the quality of education the students receive. $A$ recent poll asked 1,155 parents who have children in grades $\mathrm{K}-12$ if they were satisfied with the quality of education the students receive. Of the 1,155 surveyed, 456 indicated that they were satisfied. Construct a $99 \%$ confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. Use technology to find the $99 \%$ confidence interval. The lower bound is The upper bound is (Round to two decimal places as needed.)

Step 1 ：Given that several years ago, 34% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,155 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,155 surveyed, 456 indicated that they were satisfied.

Step 2 ：We are asked to construct a 99% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed.

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

Step 4 ：Where: p is the sample proportion, z is the z-score corresponding to the desired confidence level (for a 99% confidence level, z is approximately 2.576), and n is the sample size.

Step 5 ：In this case, the sample proportion (p) is the proportion of parents who indicated that they were satisfied, which is 456 out of 1155. The sample size (n) is 1155.

Step 6 ：Substituting these values into the formula, we get: \(p = 0.3948051948051948\), \(z = 2.576\), and \(n = 1155\)

Step 7 ：We can calculate the lower and upper bounds of the confidence interval using this formula: \(lower\_bound = 0.3577547103020518\) and \(upper\_bound = 0.43185567930833785\)

Step 8 ：Final Answer: The 99% confidence interval for the proportion of parents who are satisfied with the quality of education is approximately \(\boxed{[0.36, 0.43]}\)