Box-office ~ 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 a random sample of box-office data for movies released during the past 5 years in the USA and Canada and found that 52 out of 1254 movies with summer release date earned over 400 million dollars. They also counted that out of 540 movies released in the winter, 9 earned over 400 million dollars. Round all answers to four decimal places. Over 400 million USD Under 400 million USD Summer release 52 1202 1254 Winter release 9 531 540 1. We want to investigate whether there is a difference in the proportion of movies that earn over 400 million dollars for the two release seasons. Which hypotheses should we use? H0: The variables Release season and BOXoffice v are independent v . The difference in the proportions of movies that earned over 400 million dollars in the sample data is v due to chance. HA: The variables are not independent v . The difference in the proportions of movies that earned over 400 million dollars is not v due to chance. 2. Calculate the difference in the proportions of movies that earned over 400 million dollars: 135mm,\" Wz'nter 0.0248 3. The paragraph below describes the set up for a randomization test, if we were to conduct a hypothesis test without using software. Fill in the blanks with a number. We write Summer on 1254 cards and cards representing the movies with summer release date, and Winter on 540 cards. Then, we shuffle these cards and split them into two groups: one group of size 61 representing the movies with box- office over 400 million dollars, and another group of size 1733 representing the rest of the movies. We calculate the difference in the proportions of movies that earned over 400 million dollars during the two release seasons to get p Summer _ p Winter ' Finally, we build a histogram of these simulated differences. Use the Two Proportion Resampling Test app embedded below to do this. Use the Randomization Test for a Difference of Two Proportions app to conduct the simulation. Draw at least 3000 samples, then report your p-value from the app. Use this external link to the Randomization Test for a Difference of Two Proportions if the app does not load properly on your computer. (Right click to open in a new tab or window.) Randomization Test for a Difference of Two Proportions Controls Instructions Enter your data into the table below, or choose one of the data presets. Press Construct the Null Distribution to simulate the results under an independence null model. Graph Type Dotplot V Presets Custom V C] Show Observed Difference C] Overlay Normal Curve [3 Show Null Line A . D Show Observed Line 0 Samples Generated: 0 Count further from Enter a Value 0 Proportions of null valuev } Simulations than Number of Simulations 100 C] Show Null Distribution Information Construct the Null Distribution 4. Enter the correct values into the app and shuffle at least 3000 times. What is the approximate p-value for the hypothesis test rounded to four decimal places? p-value = | 5. Brianna uses the same hypotheses and data from a different random sample of movies to conduct this test and calculates a p- value of 0.0011. How much evidence does Brianna have that the null hypothesis model is not a good fit for her observed result? 0 A. Little 0 B. Some 0 C. Strong D. Very Strong 0 E. Extremely Strong