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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]27\%[/tex] \\
\hline
Philadelphia & [tex]46\%[/tex] \\
\hline
\end{tabular}

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

Sagot :

GinnyAnsweridn
To determine the best city for cluster sampling for the survey, we need to find out which city’s percentage of population that uses the site is closest to the overall usage percentage of the United States, which is 28%.

Here is the detailed step-by-step solution:

1. Identify the percentage usage of the site for each city:
- Denver: [tex]\(16 \%\)[/tex]
- Honolulu: [tex]\(9 \%\)[/tex]
- Miami: [tex]\(27 \%\)[/tex]
- Philadelphia: [tex]\(46 \%\)[/tex]

2. Calculate the absolute difference between the city’s percentage and the national percentage (28%):
- For Denver:
[tex]\[ |28\% - 16\%| = 12\% \][/tex]
- For Honolulu:
[tex]\[ |28\% - 9\%| = 19\% \][/tex]
- For Miami:
[tex]\[ |28\% - 27\%| = 1\% \][/tex]
- For Philadelphia:
[tex]\[ |28\% - 46\%| = 18\% \][/tex]

3. Compare these absolute differences:
- Denver: [tex]\(12\%\)[/tex]
- Honolulu: [tex]\(19\%\)[/tex]
- Miami: [tex]\(1\%\)[/tex]
- Philadelphia: [tex]\(18\%\)[/tex]

4. Determine the minimum difference:
- The smallest difference is [tex]\(1\%\)[/tex], which is for Miami.

Therefore, based on the absolute differences, the city that would be considered the best cluster to use for this survey is:
B. Miami
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