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You've provided the same context from the previous image, where we are to use Cochran's formula to calculate the sample size.

### **Cochran's Formula Recap**:
Cochran's formula is used to determine the sample size required for a survey, given a specific level of precision, confidence level, and an estimated proportion of the population.

\[
n_0 = \frac{Z^2 \cdot p \cdot (1-p)}{e^2}
\]

Given:
- \( Z = 1.96 \) (for a 95% confidence level),
- \( p = 0.37 \) (proportion of the population with the attribute, or 37%),
- \( e = 0.05 \) (margin of error, or 5%).

From our previous calculation, we found:

- Sample size \( n_0 \) using Cochran's formula is approximately **358** people.

This sample size is the recommended number of respondents to achieve a 95% confidence level with a 5% margin of error, given that 37% of the population exhibits the characteristic of interest.

Would you like more details or have any questions?

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Here are 5 related questions to consider:

1. How would the sample size change if we wanted a 99% confidence level instead of 95%?
2. What if the population proportion \( p \) was unknown—how would you modify Cochran's formula?
3. In what situations would a lower margin of error be necessary, and how would that impact the sample size?
4. What considerations should be made if the population is less than 500,000 people?
5. How would the sample size calculation differ if the survey aimed to study a rare condition (e.g., \( p \) is much lower)?

**Tip**: When using Cochran's formula, ensure that your estimated population proportion \( p \) is accurate, as it significantly influences the sample size. If uncertain, consider using a more conservative estimate to avoid under-sampling.

Learn how to use Cochran's formula to calculate the sample size needed for a survey with a 95% confidence level and a 5% margin of error. This problem involves statistical concepts and survey sampling techniques, crucial for research and data analysis.

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