# Margin of Error Calculator

An online MOE calculator with and without finite population corrections.

*Population Size (N) is a optional input. Detailed Answer

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.

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 Levelz-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%