Question

In 2013, the Pew Research Foundation reported that 45% of U.S. adults report that they live with one or more chronic conditions". However, this value was based on a sample, so it may not be a perfect estimate for the population parameter of interest on its own. The study reported a standard error of about 1.2%, and a normal model may reasonably be used in this setting. The 95% condence interval for the proportion of U.S. adults who live with one or more chronic conditions, is 43.8% to 46.2%. Which is the correct interpretaion of the confidence interval.

Since the standard error is 1.2%, only 1.2% of people in the study communicated uncertainty about their answer.
		If we repeated this study 95% of these intervals would contain the true population proportion. For example if we repeated the study1,000 times and constructed a 95% condence interval for each study, then approximately 950 of those condence intervals would contain the true fraction of U.S. adults who suffer from chronic illnesses.
		Since the standard error is only 1.2%, we can say with certainty that the population proporition of U.S. adults who suffer from a chronic illness is less than 50%.
		We can say with certainty that the population proporition of U.S. adults who suffer from a chronic illness is 43.8% to 46.2%.

Answer 1

We are given here that the 95% condence interval for the proportion of U.S. adults who live with one or more chronic conditions, is 43.8% to 46.2%.

The interpretation of this confidence interval is that the true population proportion would lie in the given confidence interval with 0.95 probability here. This means that if we repeat the study again and again, there are 95% intervals which would contain the population proportion. Therefore B is the correct answer here.