I’m working on a Mathematics question and need guidance to help me study.
Recall the use of data from the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.
Suppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. Is this much error surprising? Find the probability that a sample proportion will be an over- or underestimate of the parameter by more than 5%.