Give details about the technicality of Raosoft Sample Size Calculator ? what formulations they used
The correct answer and explanation is :
The Raosoft Sample Size Calculator is a widely used statistical tool designed to help researchers determine the minimum sample size required for a study while maintaining statistical validity. It is based on standard formulas used in survey research and statistics.
Formulations Used in Raosoft Sample Size Calculator
The calculator primarily relies on the following standard formula for determining the sample size:
[
n = \frac{Z^2 \cdot p \cdot (1 – p)}{e^2}
]
where:
- ( n ) = required sample size
- ( Z ) = Z-score (corresponding to the desired confidence level)
- ( p ) = estimated proportion of the population (default is often 0.5 for maximum variability)
- ( e ) = margin of error
If the population size (( N )) is known, the formula is adjusted as follows:
[
n’ = \frac{n}{1 + \left(\frac{n-1}{N}\right)}
]
where:
- ( n’ ) = adjusted sample size for a finite population
- ( N ) = total population size
Key Factors Considered
- Margin of Error (e): The percentage of potential error in the survey.
- Confidence Level (Z-score): Common values include:
- 90% confidence level → Z = 1.645
- 95% confidence level → Z = 1.96
- 99% confidence level → Z = 2.576
- Population Size (N): If the population is small, adjustments are necessary.
- Response Distribution (p): If unknown, it is typically set at 0.5 for conservative estimates.
This calculator is widely used in market research, healthcare, and social sciences to ensure data reliability.
