Sure, let's fill out the two-way table and solve the problem step-by-step.
Step 1: Calculate the number of people who do not pay attention to fashion.
- Total respondents: [tex]\(150\)[/tex]
- Percentage of respondents who do not pay attention to fashion: [tex]\(70\%\)[/tex]
Number of individuals who do not pay attention to fashion:
[tex]\[ 150 \times \frac{70}{100} = 105 \][/tex]
Step 2: Use the given information to fill in related parts of the table. Specifically:
- 33 of the responders who prefer neutral decorations also do not pay attention to fashion
- 20 of the responders who pay attention to fashion also prefer colorful decorations in their homes
Step 3: Calculate the number of people who do not pay attention to fashion and prefer colorful decorations.
- From the total of 105 respondents who do not pay attention to fashion, we subtract those who prefer neutral decorations (33):
Number of individuals who do not pay attention to fashion and prefer colorful decorations:
[tex]\[ 105 - 33 = 72 \][/tex]
The complete two-way table will look like this:
\begin{tabular}{|c|c|c|}
\hline & \begin{tabular}{c}
prefer colorful \\
decorations
\end{tabular} & \begin{tabular}{c}
prefer neutral \\
decorations
\end{tabular} \\
\hline \begin{tabular}{c}
pay attention to \\
fashion
\end{tabular} & 20 & \\
\hline \begin{tabular}{c}
do not pay attention \\
to fashion
\end{tabular} & 72 & 33 \\
\hline
\end{tabular}
Finally, the number of sampled people who do not pay attention to fashion and prefer colorful decorations is:
[tex]\[ 72 \][/tex]
