Final answer:
The 95% confidence interval for the support of banning smoking in all public places in 2011 is between 55% and 63%, taking the 59% reported percentage and accounting for the 4% margin of error.
Step-by-step explanation:
The confidence interval for the population percentage that supported banning smoking in all public places in 2011 is 55% to 63%. This interval is calculated by taking the sample percentage (59%) and adding and subtracting the margin of error (4 percentage points).The confidence interval for the proportion of U.S. adults who would support banning smoking in all public places in 2011 is 55% to 63%. This means that we are 95% confident that the true population percentage falls within this range.
Explaining in detail, a confidence interval provides a range within which we can be fairly certain the true population parameter lies, given a certain level of confidence. In this case, with a 95% confidence interval, we are saying that if we were to sample the population many times and calculate the confidence interval each time, 95% of those intervals would contain the true percentage of the population supporting the ban on smoking in public places. It's also significant that the margin of error is at a practical level, giving a precise yet reliable range for decision-making purposes.