Test audiences screened five 3-minute previews of a certain movie. The movie contains both drama and comedy, but the previews...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

1. A higher percentage of comedy in the preview (\(\mathrm{C}\)) strongly increases the percent of audience members who find it funny (\(\mathrm{F}\)), showing a clear positive correlation between \(\mathrm{C}\) and \(\mathrm{F}\).
2. The highest reported likelihood to see the movie (\(\mathrm{L}\)) is at a moderate, not extreme, comedy level, suggesting audience interest peaks with a mix of comedy and drama.
3. Increasing drama necessarily reduces comedy (since \(\mathrm{C + D = 100}\)), so drama percentage (\(\mathrm{D}\)) negatively correlates with \(\mathrm{F}\) and with anticipated movie attendance.

Step-by-Step Solution

Question 1: Variables That Could Differ with Different Audiences

Complete Statement:

If the same previews were shown to other test audiences, ______ could differ from the results shown.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: same previews
    Meaning: Refers to using the identical 3-minute preview videos as were previously tested.
    Relation to Chart: Each bubble represents a specific preview's fixed content on the chart.
    Important Implications: The percentage of comedy (\(\mathrm{C}\)) in each preview does not change regardless of audience.

• Statement Breakdown 2:
  • Key Phrase: other test audiences
    Meaning: Refers to different groups of people watching the same previews.
    Relation to Chart: Current chart is based on one audience; a new audience might produce different results.
    Important Implications: Variables reliant on opinions or preferences could differ between audiences.

• What is needed: Which variables shown (\(\mathrm{C}\), \(\mathrm{F}\), and \(\mathrm{L}\)) might change if different audiences were shown the same previews.

Solution:

• Condensed Solution Implementation:
  Identify which variables are inherent to the previews (fixed) versus those dependent on audience opinions (variable).
• Necessary Data points:
  \(\mathrm{C}\) = percent comedy (fixed by preview content), \(\mathrm{F}\) = percent who found preview funny (audience-dependent), \(\mathrm{L}\) = likelihood to see movie (audience-dependent).
  • Calculations Estimations:
    No calculation required; logical classification between fixed content and audience response.
  • Comparison to Answer Choices:
    \(\mathrm{C}\) does not change. \(\mathrm{F}\) and \(\mathrm{L}\) would change with a different audience. Therefore, only \(\mathrm{F}\) and \(\mathrm{L}\) could differ.

FINAL ANSWER Blank 1: only F and L

Question 2: Correlation Between Drama Percentage and 'Finding Funny' Percent

Complete Statement:

Let \(\mathrm{D}\) equal the percent of drama in each preview. Assuming each preview is made up entirely of comedy and drama (such that \(\mathrm{C + D = 100}\)), there is ______ correlation between \(\mathrm{D}\) and \(\mathrm{F}\).

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: D equal the percent of drama
    Meaning: \(\mathrm{D}\) is defined as the percent of dramatic content in each preview.
    Relation to Chart: \(\mathrm{D}\) does not appear on the chart but can be calculated as \(\mathrm{D = 100 - C}\).

• Statement Breakdown 2:
  • Key Phrase: C + D = 100
    Meaning: Previews are made only of comedy and drama; their percentages sum to 100%.
    Relation to Chart: If \(\mathrm{C}\) is given for a bubble, \(\mathrm{D}\) is determined automatically.

• What is needed: Whether the correlation between percent drama (\(\mathrm{D}\)) and percentage finding it funny (\(\mathrm{F}\)) is positive, negative, or none.

Solution:

• Condensed Solution Implementation:
  Since \(\mathrm{D = 100 - C}\), increasing \(\mathrm{D}\) means decreasing \(\mathrm{C}\). The chart shows that as \(\mathrm{C}\) (comedy) increases, \(\mathrm{F}\) (funny) increases. Therefore, as \(\mathrm{D}\) increases, \(\mathrm{F}\) decreases.
• Necessary Data points:
  Positive correlation exists between \(\mathrm{C}\) and \(\mathrm{F}\); \(\mathrm{D}\) is the complement of \(\mathrm{C}\).
  • Calculations Estimations:
    As \(\mathrm{D}\) rises (\(\mathrm{C}\) falls), \(\mathrm{F}\) falls (since higher comedy leads to higher funny percentage). Thus, negative correlation.
  • Comparison to Answer Choices:
    Since \(\mathrm{F}\) decreases as \(\mathrm{D}\) increases (opposite directions), this is a negative correlation.

FINAL ANSWER Blank 2: a negative

Summary

For Blank 1, only audience-dependent variables (\(\mathrm{F}\) and \(\mathrm{L}\)) could differ with new audiences; \(\mathrm{C}\) is determined by preview content. For Blank 2, since \(\mathrm{D}\) increases as \(\mathrm{C}\) decreases, and \(\mathrm{C}\) has a positive relationship with \(\mathrm{F}\), \(\mathrm{D}\) and \(\mathrm{F}\) are negatively correlated.

Question Independence Analysis

Both blanks are independent. The first targets variable dependence on audience, while the second addresses mathematical correlation; neither answer depends on the other.