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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

Sagot :

GinnyAnswer
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
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