Question

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 1258 movies with summer release date earned over 400 million dollars. They also counted that out of 545 movies released in the winter, 8 earned over 400 million dollars.
Over 4 million USD Under 4 million USD
Summer release 57 1251
Winter release 11 544
Total
1. We want to investigate whether there is a difference in the proportion of movies that eam over 400 million dollars for the two release seasons. Which hypotheses should we use?
2. Calculate the difference in the proportions of movies that eamed over 400 million dollars.
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_____cards and cards representing the movies with summer release date, and Winter on_____cards. Then, we shuffle these cards and split them into two groups one group of size_____representing the movies with box-office over 400 million dollars, and another group of size_____representing the rest of the movies. We calculate the difference in the proportions of movies that eaned over 400 million dollars during the two release seasons to get PSmmer PWinter. Finally, we build a histogram of these simulated dfterences.

Answer 1

Answer:

Step-by-step explanation:

                           Over 4 million USD    Under 4 million USD    Total

Summer release      57                               1195                         1251

Winter release         11                                533                           544

1)Let $P_1$ be the proportion of movies that earn over 400 million in summer and $P_2$ be the proportion of movies that earn over 400 million in winter.

Null hypothesis:$H_0:P_1= P_2$

Alternate hypothesis : $H_a: P_1 \neq P_2$

2)Calculate the difference in the proportions of movies that earned over 400 million dollars.

$P_1=\frac{57}{1251}=0.045$

$P_2=\frac{11}{544}=0.0202$

3)

$P_{(Summer)}-P_{(winter)}=0.045-0.0202=0.0248$

We write Summer on 1251 cards and cards representing the movies with summer release date, and Winter on 544 cards. Then, we shuffle these cards and split them into two groups one group of size 68 representing the movies with box-office over 400 million dollars, and another group of size representing 1728 the rest of the movies.