You may need to use the appropriate appendix table or technology to answer this question.

For many years, businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health$-$care prices and employees paying for a larger portion of health care benefits. A recent survey showed that $58\%$ of employers are likely to require higher employee contributions for health$-$care coverage this year relative to last year. Suppose the survey was based on a sample of $800$ companies likely to require higher employee contributions for health$-$care coverage this year relative to last year.

At $95\%$ confidence, compute the margin of error for the proportion of companies likely to require higher employee contributions for health$-$care coverage. $($Round your answer to four decimal places.$)$

Compute a $95\%$ confidence interval for the proportion of companies likely to require higher employee contributions for health$-$care coverage. $($Round your answers to four decimal places.$)$