A Gallup Poll found that 51% of the people in its sample said "Yes" when asked, "Would you like to lose weight?" Gallup announced: "For results based on the total sample of national adults, one can say with 95% confidence that the margin of sampling error is 3 percentage points."
(a) What is the 95% confidence interval for the percent of all adults who want to lose weight?
(b) What does it mean to say that we have 95% confidence in this interval?