Exercise 9

Chronic illness, Part II. In 2013, the Pew Research Foundation reported that “45% of U.S. adults report that they live with one or more chronic conditions”, and the standard error for this estimate is 1.2%. Identify each of the following statements as true or false. Provide an explanation to justify each of your answers.

1. We can say with certainty that the confidence interval from Exercise 5.7 contains the true percentage of U.S. adults who suffer from a chronic illness.

2. If we repeated this study 1,000 times and constructed a 95% confidence interval for each study, then approximately 950 of those confidence intervals would contain the true fraction of U.S. adults who suffer from chronic illnesses.

3. The poll provides statistically significant evidence (at the $\alpha=0.05$ level) that the percentage of U.S. adults who suffer from chronic illnesses is below 50%.

4. Since the standard error is 1.2%, only 1.2% of people in the study communicated uncertainty about their answer.