Post Test: Relating Data Sets

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 two-way table indicate the numbers of viewers who rated the film on a four-point scale: excellent, good, average, and poor.

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

Select the correct answer:

What percentage of the audience from the [tex]$16-25$[/tex] age group gave the movie a poor rating?

A. [tex]$6.19 \%$[/tex]

B. [tex]$1000 \%$[/tex]

C. [tex]$25.34 \%$[/tex]

D. [tex]$15.70 \%$[/tex]

E. [tex]$16.22 \%$[/tex]

To find the percentage of the audience from the 16-25 age group who gave the movie a poor rating, follow these steps:

1. Identify the number of viewers in the 16-25 age group who rated the movie as "Poor":
- From the table, we can see that 7 viewers in the 16-25 age group gave the movie a "Poor" rating.

2. Determine the total number of viewers in the 16-25 age group:
- According to the table, there are 113 viewers in total in the 16-25 age group.

3. Calculate the percentage of "Poor" ratings:
- To find the percentage, divide the number of "Poor" ratings by the total number of viewers in that age group, and then multiply by 100 to convert it to a percentage.
[tex]\[
\text{Percentage of Poor ratings} = \left(\frac{7}{113}\right) \times 100
\][/tex]

4. Compute the result:
- After performing this calculation, you find that approximately 6.19% of the audience in the 16-25 age group gave the movie a "Poor" rating.

Therefore, the correct answer is:
A. 6.19%