Let's continue exploring Academy Award Nominees for Best Picture. The data set contains information for a random sample of 348 nominees for the Academy Award for Best Picture.
Here's a two-way table to examine the relationship between these two categorical variables: result (Nominee or Winner) and rating (G, PG, PG-13, etc.).
Based on the two-way table, we can compute the following statistics (sample proportions):
The proportion of movies that win the Academy Award for Best picture among nominees rated PG is 0.22 ( or 15/68).
The proportion of movies that win the Academy Award for Best picture among nominees rated-PG-13 is 0.15 ( or 10/66).
Based on the data, we see that these two observed sample proportions are different; one is higher than the other. But is this difference significant? Apply your understanding of hypothesis tests to assess if the population proportion of winners among rated-PG nominated movies (group 1) is higher when compared to rated-PG-13 nominated films (group 2)?
a.) State the appropriate hypotheses. Remember to use the proper notation.
b.)