The Walt Disney Company, the production studio behind the Marvel Cinematic Universe, is trying to find the best release date for their new super hero movie. They are hesitating between the summer and winter holiday release, and they want to know if there is any difference between the earning potential during those seasons. The analytics division in the company examined box-office data for movies released during the past 5 years in the USA and Canada and found that 56 out of 1259 movies with summer release date earned over 400 million dollars. They also counted that out of 540 movies released in the winter, 10 earned over 400 million dollars. Round all answers to four decimal places.

Over 400 million USD Under 400 million USD Total
Summer release 54 1252
Winter release 6 547
Total

a. What are the hypotheses for testing whether there is a significant difference in the proportion of movies who earn over 400 million dollars for the two release seasons?
b. Calculate the difference in the proportions of movies that earned over 400 million dollars.