Sample size (n):
Conversion steps:
n = N / (1 + N × e2)
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:
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.