To determine how many people Mickey should include in her survey, we can use the concept of sampling. A common rule of thumb in survey sampling is to ensure a representative sample. A general guideline is to survey at least 10% of the population to get a reasonably accurate representation, but in many cases, especially for larger populations, a smaller percentage might suffice.
For Mickey's gym with 450 members:
-
Calculating 10% of the population:
\[ 10% \text{ of } 450 = 0.10 \times 450 = 45 \]
Under usual circumstances, surveying 45 members would be a good start to get a representative view of the opinions of the entire gym membership.
- Considering if a smaller sample is reliable:
In practice, surveys can still be effective with smaller samples, especially if randomness is implemented in how those members are chosen. However, to ensure that her results are statistically reliable, a larger sample size might be more beneficial.
A common reliable sample size for surveys is around 30 responses — essential for statistical validity but may not yield a broad view.
In light of balancing robustness in results with practicality, the least number of people Mickey should include is:
\[ \boxed{45} \]
This number ensures she gets a good sampling while also being statistically valid for the larger population of 450 gym members.