Sample Size Margin Error (ME) Calculator
Margin of Error Calculator
An online MOE calculator with and without finite population corrections.
MOE Formula
= z * √p * (1 - p) / √n
Where: z is z-score (a critical value) for a confidence level Percentage,
p = proportion,
N = population size,
n = sample size.
MOE Formula (with finite Population Correction)
= z * √p * (1 - p) / √(N - 1) * n / (N - n)
Where: z is z-score (a critical value) for a confidence level Percentage,
p = proportion,
N = population size,
n = sample size.
More information
Population Size: The total number of people whose opinion or behaviour your sample will represent.
Confidence Level (%): The Probability that your sample accurately reflects the attitudes of your population.The industry standard is 95%.
Sample Size:Number of people who look your survey.
Margin of Error (%): The range (measured as a percentage) that your populations response may deviate from your samples.
z value
Our calculator used the following z-score values.
| Confidence Level | z-score |
|---|---|
| 70% | 1.04 |
| 75% | 1.15 |
| 80% | 1.28 |
| 85% | 1.44 |
| 90% | 1.645 |
| 91% | 1.7 |
| 92% | 1.75 |
| 93% | 1.81 |
| 94% | 1.88 |
| 95% | 1.96 |
| 96% | 2.05 |
| 97% | 2.17 |
| 98% | 2.33 |
| 99% | 2.576 |
| 99.5% | 2.807 |
| 99.9% | 3.29 |
| 99.99% | 3.89 |
MOE Real Time Example Question and Derivation:
1000 people were surveyed and 380 thought that natural disasters was not caused by human pollution.
Find the Margin of Error for a 90% confidence interval ?
Step 1:Find P-hat by dividing the number of people who responded positively. In this case, 380/1000 people (38%) responded positively.
Step 2:Find the z-score that goes with the given confidence interval 90% , you get a z-score (a critical value) of 1.645.
Step 3:Insert the values into the formula and solve:
MOE = z * √p * (1 - p) / √(N - 1) * n / (N - n)
Where: z = 1.645, Proportion Percentage (P) = 38% Sample size (n) = 1000 evel of 90%
MOE = 1.645 * √0.38 * (1-0.38)/ √1000
MOE = 0.798/31.623 * 100
The margin of error is ±2.525%
See Also ►
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Percentile,Ordinal Rank Calculator
P Value from Z score Calculator
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PERT Expected Time Probability Calculator
Mean Median Mode Ranges Calculator