Sample size (n):

200

Conversion steps:

n = N / (1 + N × e^{2})

n = 400 / (1 + 400 × (0.05)^{2})

n = 400 / (1 + 400 × 0.0025)

n = 400 / (1 + 1)

n = 400 / (2)

n = 200

∴ Sample size (n) = 200

Slovin's Formula is a statistical method used to determine the sample size needed for a survey or research project. It helps researchers decide how many participants are required to achieve a specific level of accuracy and confidence in their results. The formula is particularly useful when dealing with large populations where it is impractical to survey every individual.

The formula for Slovin's is:

**n = N / (1 + Ne2)**

Where:

- nnn = Sample size
- NNN = Population size
- eee = Margin of error (expressed as a decimal)

**Enter Population Size (N):**Input the total number of individuals in the population you are studying.**Enter Desired Margin of Error (e):**Input the margin of error you are willing to accept for your survey results. Common values range from 0.01 to 0.10, with 0.05 being a typical choice for a 95% confidence level.**Calculate Sample Size:**Click the "Calculate" button to compute the required sample size using Slovin's Formula Calculator.

Suppose you want to conduct a survey in a town with a population of 10,000 people and you are comfortable with a margin of error of 5% (0.05).

**Using Slovin's Formula:**

n=10000/1+10000(0.052)

n=10000/1+10000(0.0025)

n=10000/1+25

n=10000/26

n≈385

You would need to survey approximately 385 people to achieve your desired accuracy.