calculate the sample size of the population size (N) 340 then margin of error (e) 0.04 using yamane's formula

To calculate the sample size using Yamane's formula, you can use the following formula:

\[
n = \frac{N}{1 + N(e^2)}
\]

Where:
- \( n \) is the sample size,
- \( N \) is the population size,
- \( e \) is the margin of error (expressed as a decimal).

Given:
- Population size \( N = 340 \)
- Margin of error \( e = 0.04 \)

Substituting the values into the formula:

\[
n = \frac{340}{1 + 340(0.04^2)}
\]

Let's calculate it.

\[
n = \frac{340}{1 + 340(0.0016)} = \frac{340}{1 + 0.544} = \frac{340}{1.544} \approx 220.23
\]

So, the required sample size \( n \) is approximately **220**.

Would you like any further details or explanations on this calculation?

Here are some related questions you might consider:
1. How does the margin of error affect the sample size?
2. What if the population size is larger or smaller—how does that impact \( n \)?
3. How does Yamane’s formula compare to other sample size formulas?
4. What if the margin of error is decreased to 0.02, how would that affect the sample size?
5. What happens to the sample size if the population is assumed to be infinite?

**Tip:** Always round up the sample size to ensure the margin of error doesn't increase.

Learn how to calculate the sample size for a population of 340 with a 0.04 margin of error using Yamane's formula. This solution covers essential concepts in statistics, including error margins and sampling theory, making it suitable for undergraduate students.

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