In the legendary Theater District in New York, gross profits from 38 new productions were over $1.8 Billion for the 2018/19 season, a large gain from the $1.4 Billion gross profits from 45 productions only two years prior, in the 2016/17 season. However, this may be due to a change in the type of production, as the cost of attending plays has increased, while the cost of attending musicals has not. The goal of this assignment is to answer the following research question: Has the proportion of Broadway productions that are plays increased since the 2016/17 season? To help answer this research question, data published by Broadway League, has provided the following information:

● Base Rate: The number of plays in the 2016/17 season is 20 out of a total of 45 productions. 

● Observed Data: The number of plays in the 2018/19 season is 21 out of a total of 38 productions.

1. Does the observed percentage suggest that the proportion of productions that are plays has increased? Explain your reasoning. Model To answer the research question, you will set up a TinkerPlots sampler that models the variation in production types that you would expect in 2018 using the base rate from the 2016/17 season. 

2. Set up a TinkerPlots sampler that corresponds to the model that is described above. Copy and paste or sketch the sampler window into your word-processed document.

3. Write the statistical hypothesis that describes the model in your TinkerPlots sampler.

Simulate from the ModelUse TinkerPlots to generate the 500 samples of seasons' productions. Collect the percent of productions that are plays from each trial of the simulation. Evaluate the Observed Results

4. Use formal statistical language to describe the shape of the distribution of simulated results.

5. Compute and report the mean percent of productions that are plays that is expected under the hypothesized model. Explain how this relates to the statistical hypothesis you wrote in Question #2.

6. Compute and report the standard deviation and use it to determine a range of likely values. Show your work.

7. Use TinkerPlotsto add a reference line on your plot of 500 trials at the observed value and add a divider to the plot to show the range of likely values. Copy and paste your plot with the reference line and divider or draw a rough outline of your plot below.

8. Based on the variation you described in Question #6 and your observed value, is the observed result from the 2018/19 season compatible under the hypothesized model? Explain.

9. Write a short note to Broadway Production executives that answers the research question. In your response, use the statistical evidence from your simulation to explain how you came to the conclusion you did.