Context

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.

Prompt

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. In this random sample, the sample proportion (25%) differs from the estimated population proportion (30%) by 5%. In other words, there is a 5% error in the sample proportion; this sample under-estimates the population proportion by 5%.

Is this much error surprising? To answer this question, find the probability that a sample proportion will over- or under-estimate the parameter by more than 5%.

Show your work by checking normality conditions, calculating a z-score, explaining how the area under the normal curve is used to answer the question, and stating a conclusion in the context of this problem.

free normal distribution calculator link: https://cerritos.instructure.com/courses/39623/pages/applet-normal-distribution-calculator-input-one-z-score