Using these parameters, we can calculate the required sample size using the following formula:n=z2∗p(1−p)e2n=e2z2∗p(1−p)Where:
- n is the sample size
- z is the z-score for the desired confidence level (2.576 for 99% confidence)
- p is the population proportion (0.5)
- e is the margin of error (0.05)
Plugging in these values:n=2.5762∗0.5(1−0.5)0.052≈663.57n=0.0522.5762∗0.5(1−0.5)≈663.57
Recommendation
Based on this calculation, you should aim to take approximately 664 readings to achieve a 99% confidence level with a 5% margin of error.
Considerations
- Precision vs. Practicality: While 664 readings provide high confidence, consider if this number is practical for your specific situation.
- Diminishing Returns: There's a point of diminishing returns where increasing sample size provides minimal improvements in confidence.
- Accuracy vs. Confidence: Note that increasing the number of readings improves confidence in your results but doesn't necessarily improve the accuracy of individual readings.
- Variability: If your readings have low variability, you might achieve high confidence with fewer samples.