In: Statistics and Probability
In 1955, John Wayne played Genghis Khan in a movie called The Conqueror. The movie was filmed downwind of the site of eleven previous above-ground nuclear bomb tests. Of the 220 people who worked on the movie, 91 were diagnosed with cancer by the early 1980s, including Wayne, his co-stars, and the director. According to a large-scale epidemiological study, only ~14% of the general populace of similar age develop cancer. (Assume this probability relates to each of the movie people). Is there evidence for an increased cancer risk for people associated with the movie.
What is the best estimate of the probability of a movie person getting cancer within the study interval? What is the standard error of your estimate? What does this quantity measure? What is the 95% confidence interval for this probability estimate? Does this interval bracket the typical cancer rate of 14% from the large-scale study of the general populace? Interpret the result.