question 15

It is a well known fact that ST311 instructor Nic is both a dedicated staring contest participant and a firm believer in astrology. He wonders if his odds of winning a given staring contest are better if he's competing against a Scorpio or if he's competing against a Virgo. To answer this question, he combs through his very detailed notes, taking two simple random samples: one of the staring contests he has participated in against Scorpios and one of staring contests he's participated in against Virgos. Because Nic has had extensive statistical training, he makes sure that his samples are independent. He finds that he has won 37 out of 55 staring contests with Virgos and 32 out of 68 staring contests with Scorpios. What is the margin of error for a 99% confidence interval for the difference that Nic is interested in? Please give your answer rounded to 3 digits after the decimal place. If conditions necessary to perform the calculation have not been met, input -1 as your