Answered

Find the best solutions to your problems with the help of IDNLearn.com's expert users. Receive prompt and accurate responses to your questions from our community of knowledgeable professionals ready to assist you at any time.

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. Honolulu
B. Philadelphia
C. Denver
D. Miami

Sagot :

GinnyAnsweridn
Let's analyze the given percentages of social networking site usage in different cities and determine which city would be the best cluster to use for a survey. This will be done by finding which city's percentage is closest to the overall 28% usage in the United States.

Here's the data provided:
- Denver: 16%
- Honolulu: 9%
- Miami: 27%
- Philadelphia: 46%

We start by calculating the absolute difference between the percentage of each city and the overall 28% for the United States.

1. Denver:
- Percentage of usage: 16%
- Difference from 28%: [tex]\( |16\% - 28\%| = | -12\% | = 12\% \)[/tex]

2. Honolulu:
- Percentage of usage: 9%
- Difference from 28%: [tex]\( |9\% - 28\%| = | -19\% | = 19\% \)[/tex]

3. Miami:
- Percentage of usage: 27%
- Difference from 28%: [tex]\( |27\% - 28\%| = | -1\% | = 1\% \)[/tex]

4. Philadelphia:
- Percentage of usage: 46%
- Difference from 28%: [tex]\( |46\% - 28\%| = | 18\% | = 18\% \)[/tex]

Now we compare the differences calculated:
- Denver: 12%
- Honolulu: 19%
- Miami: 1%
- Philadelphia: 18%

The city with the smallest difference from the overall percentage (28%) is Miami, with a difference of just 1%.

Thus, the best city to choose as a cluster for the survey to most closely represent the 28% usage in the United States is:

D. Miami
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.