calculate the sample size of the population size (N) 560 then margin of error (e) 0.07 using yamane's formula

Yamane's formula is used to calculate sample sizes with a given population size and a margin of error. The formula is as follows:

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

Where:
- \( n \) = sample size
- \( N \) = population size
- \( e \) = margin of error

Given:
- \( N = 560 \)
- \( e = 0.07 \)

Now, substitute these values into the formula:

\[
n = \frac{560}{1 + 560 \cdot (0.07)^2}
\]

First, calculate \( e^2 \):

\[
e^2 = 0.07^2 = 0.0049
\]

Next, calculate the denominator:

\[
1 + 560 \cdot 0.0049 = 1 + 2.744 = 3.744
\]

Now, divide the population size by the result:

\[
n = \frac{560}{3.744} \approx 149.61
\]

Since the sample size should be a whole number, round it to the nearest whole number:

\[
n \approx 150
\]

So, the sample size is **150**.

Would you like more details or have any questions?

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Here are 5 related questions to consider:
1. How does changing the margin of error affect the sample size?
2. What would the sample size be if the margin of error were 0.05 instead of 0.07?
3. How does Yamane's formula compare to other sample size calculation methods?
4. Why is it important to round up the sample size?
5. How does the population size impact the sample size in Yamane's formula?

**Tip:** When calculating sample size, always round up to ensure that your sample is large enough to maintain the desired margin of error.

Learn how to calculate the sample size for a population of 560 using Yamane's formula with a margin of error of 0.07. This problem demonstrates essential statistical concepts like sample size calculation and margin of error. Suitable for undergraduate statistics students.

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