Answered

A movie producer conducted a survey after the screening of his movie to find out how the film would be received by viewers from different age groups. The columns in the table indicate the numbers of viewers who rated the film on a four-point scale: excellent, good, average, and poor.

\begin{tabular}{|c|c|c|c|c|c|}
\hline Viewer's Age Group & Excellent & Good & Average & Poor & Marginal Totals \\
\hline [tex]$16-25$[/tex] & 52 & 42 & 12 & 7 & 113 \\
\hline [tex]$26-35$[/tex] & 33 & 50 & 5 & 9 & 97 \\
\hline [tex]$36-45$[/tex] & 58 & 12 & 28 & 34 & 132 \\
\hline [tex]$46-55$[/tex] & 25 & 17 & 22 & 12 & 76 \\
\hline [tex]$56$[/tex] and Above & 12 & 5 & 3 & 8 & 28 \\
\hline Marginal Totals & 180 & 126 & 70 & 70 & 446 \\
\hline
\end{tabular}

Select the correct answer:
Which of these observations is supported by the data in the table?
(Note: A rating of good or excellent means the audience liked the movie, while a rating of poor means the audience disliked the movie.)

A. The majority of the audience in the [tex]$26-35$[/tex] age group liked the movie.
B. Among those who liked the movie, the majority were in the oldest age group.
C. Among those who disliked the movie, the majority were in the [tex]$26-35$[/tex] age group.
D. The majority of the audience in the [tex]$16-25$[/tex] age group liked the movie.
E. The majority of the audience from all the age groups disliked the movie.



Answer :

GinnyAnswer
To determine which of the given statements is supported by the data in the table, we will analyze each option step-by-step using the provided data.

First, let's recall the key information needed for this analysis:
1. People who rated the movie as "Excellent" or "Good" liked the movie.
2. People who rated the movie as "Poor" disliked the movie.

Now, let's break down each option:

### Option A: The majority of the audience in the [tex]\(26-35\)[/tex] age group did not like the movie.
- Total in [tex]\(26-35\)[/tex] age group: 97.
- Liked the movie (Excellent + Good): [tex]\(33 + 50 = 83\)[/tex].
- Disliked the movie (Poor): [tex]\(9\)[/tex].
The majority (more than half) of the [tex]\(26-35\)[/tex] age group liked the movie since 83 is greater than half of 97 (48.5). Therefore, this statement is false.

### Option B: Among those who liked the movie, the majority were in the oldest age group.
- Total who liked the movie in [tex]\(56\)[/tex] and Above age group: [tex]\(12 + 5 = 17\)[/tex].
- Total who liked the movie across all age groups: [tex]\(180 + 126 = 306\)[/tex].
The number of people in the oldest age group who liked the movie (17) is not the majority of 306. Therefore, this statement is false.

### Option C: Among those who disliked the movie, the majority were in the [tex]\(26-35\)[/tex] age group.
- Total who disliked the movie in [tex]\(26-35\)[/tex] age group: [tex]\(9\)[/tex].
- Total who disliked the movie across all age groups: 70.
The number of people in the [tex]\(26-35\)[/tex] age group who disliked the movie (9) is not the majority of 70. Therefore, this statement is false.

### Option D: The majority of the audience in the [tex]\(16-25\)[/tex] age group liked the movie.
- Total in [tex]\(16-25\)[/tex] age group: 113.
- Liked the movie (Excellent + Good): [tex]\(52 + 42 = 94\)[/tex].
The majority (more than half) of the [tex]\(16-25\)[/tex] age group liked the movie since 94 is greater than half of 113 (56.5). Therefore, this statement is true.

### Option E: The majority of the audience from all the age groups disliked the movie.
This means considering each age group individually:
- [tex]\(16-25\)[/tex] age group: 7 disliked out of 113.
- [tex]\(26-35\)[/tex] age group: 9 disliked out of 97.
- [tex]\(36-45\)[/tex] age group: 34 disliked out of 132.
- [tex]\(46-55\)[/tex] age group: 12 disliked out of 76.
- [tex]\(56\)[/tex] and Above age group: 8 disliked out of 28.
None of the age groups have the majority disliking the movie. Therefore, this statement is false.

Since the correct observation supported by the data in the table is Option D: The majority of the audience in the [tex]\(16-25\)[/tex] age group liked the movie.