Suppose cluster sampling were being used to survey users of a particular social networking site. [tex]28 \%[/tex] of the entire population of the United States uses this site. Based on the table below, which city would be considered the best cluster to use for this survey?

\begin{tabular}{|c|c|}
\hline
City & \begin{tabular}{c}
Percentage of population \\
that uses site
\end{tabular} \\
\hline
Denver & [tex]16 \%[/tex] \\
\hline
Honolulu & [tex]9 \%[/tex] \\
\hline
Miami & [tex]46 \%[/tex] \\
\hline
Philadelphia & [tex]27 \%[/tex] \\
\hline
\end{tabular}

A. Miami
B. Honolulu
C. Denver
D. Philadelphia



Answer :

To determine the best city for cluster sampling, we need to find the city whose percentage of population using the social networking site is closest to the overall percentage of 28%.

Here are the given percentages:

- Denver: 16%
- Honolulu: 9%
- Miami: 46%
- Philadelphia: 27%

We will compare how close each city's percentage is to the overall 28% by calculating the absolute difference between each city's percentage and 28%.

1. Denver:
[tex]\[ |28\% - 16\%| = 12\% \][/tex]

2. Honolulu:
[tex]\[ |28\% - 9\%| = 19\% \][/tex]

3. Miami:
[tex]\[ |28\% - 46\%| = 18\% \][/tex]

4. Philadelphia:
[tex]\[ |28\% - 27\%| = 1\% \][/tex]

Next, we compare these differences:
- Denver: 12%
- Honolulu: 19%
- Miami: 18%
- Philadelphia: 1%

The smallest absolute difference is 1%, which corresponds to Philadelphia. Therefore, Philadelphia's percentage of 27% is closest to the overall percentage of 28%.

Conclusion:

The best city for cluster sampling is:
D. Philadelphia