Question: Going to church. Opinion polls show that about 40% of Americans say they attended religious services in the last week. This result has stayed stable for decades. Studies of what people actually do, as opposed to what they say they do, suggest that actual church attendance is much lower. One study calculated 95% confidence intervals based on what a sample of Catholics said and then based on a sample of actual behavior. In Chicago, for example, the 95% confidence interval from the opinion poll said that between 45.7% and 51.3% of Catholics attended mass weekly. The 95% confidence interval from actual counts said that between 25.7% and 28.9% attended mass weekly.
(a) Why might we expect opinion polls on church attendance to be biased in the direction of overestimating true attendance?
(b) The poll in Chicago found that 48.5% of Catholics claimed to attend mass weekly. Why don't we just say that "48.5% of all Catholics in Chicago claim to attend mass" instead of giving the interval 45.7% to 51.3%?
(c) The two results, from reported and observed behavior, are quite different. What does it mean to say that we are "95% confident" in each of the two intervals given?