In 1955, John Wayne played Genghis Khan in a movie called The Conqueror. It was not an artistic success. More unfortunately, the movie was filmed downwind of the site of 11 previous aboveground nuclear bomb tests. Of the 220 people who worked on this movie, 91 had been diagnosed with cancer by the early 1980s, including Wayne, his costars, and the director. According to large-scale epidemiological data, only about 14% of people of this age group, on average, should have been stricken with cancer within this time frame. We want to know 7 whether there is evidence for an increased cancer risk for people associated with this film.

Assume that this probability is the same for each member of the cast.

a. What is the best estimate of the probability of a member of the cast or crew getting cancer within the study interval?

b. What is the standard error of your estimate? What does this quantity measure?

c. What is the 95% confidence interval for this probability estimate? Does this interval bracket the typical cancer rate of 14% for people of the same age group? Interpret this result.