The working principle of the margin of error calculator is very easy;
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The margin of error calculates the MOE using sample size (n), population size (P), sample proportion (p), and confidence level. It gives a step-by-step solution to the problem.
The margin of error (MOE) for a survey tells you ways close you'll be able to expect the survey results to be to the proper population price. E.g., In a random survey, we came to know that 55% of the population favored Brand X over Brand Y with 2% MOE.
According to this survey, the actual population percentage that voted for Brand X falls within the range of 55% ± 2%. MOE refers to the degree of error in the results that we get from surveys of random sampling.
There are two different cases to calculate the margin of error of a raw sample.
The formula to calculate the MOE with FPC is as follows:
MOE with finite population correction :
Now let’s have a look at the FPC, in the sample survey statistics, this concept plays a vital role. It is a factor that is used to balance the estimated variance for a hypothetical total or mean.
In the above formula,
The simple MOE can be calculated using the following formula:
In this section, with the assistance of examples, the procedure is explained briefly.
Example 1:
Calculate the MOE with FPC if the sample proportion is 0.2, the population size is 1029, the sample size is 112, and the confidence interval is 95%.
Solution:
Step 1: Extract the data
Sample proportion = = 0.2
Population size = p = 1029
The confidence interval of z at 95% = 1.960
Sample size = n = 112
Step 2: enter the values in the following formula
MOE with FPC =
MOE with FPC = 1.960 {{0.2 (1 - 0.2)}/ {112(1029 – 1)/ (1029 – 112)}
MOE with FPC = 1.960 {0.2 (0.8) / {(112) * (1028) / (917)}}}
MOE with FPC = 1.960 { 0.2(0.8)/ {112(1.121)}
MOE with FPC = 1.960 {0.16/ {125.55}}
MOE with FPC = 1.960 * 0.03569761
MOE with FPC = 0.06996
MOE with FPC = 6.997%
Margin of error | Statistics How To.
Your guide to margin of error | Qualtrics.
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