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