Find Margin of Error
MOE = 1 / square root of n
Margin of error is a statistical term referring to the amount of random sampling error in a survey’s results. It is calculated by taking the standard error of a proportion or mean and multiplying it by a critical value that corresponds to a desired level of confidence.
The margin of error formula is:
Margin of error = critical value x standard error
Where the critical value is determined by the level of confidence chosen (typically 95% or 99%), and the standard error is calculated using the sample size and the population parameter being estimated (e.g. proportion or mean).
Here is an example of how to calculate the margin of error:
Suppose we want to estimate the proportion of adults in a city who support a new law, and we take a random sample of 500 adults. The sample proportion who support the law is 0.60, and we want to be 95% confident that the true proportion is within plus or minus 3% of the sample proportion.
To find the margin of error, we need to first calculate the standard error:
standard error = sqrt(p*(1-p)/n)
where p is the sample proportion (0.60) and n is the sample size (500).
standard error = sqrt(0.60*(1-0.60)/500) = 0.0245
Next, we need to find the critical value from a standard normal distribution table (or calculator) at the 95% confidence level. The critical value is 1.96.
Finally, we can calculate the margin of error:
margin of error = 1.96 x 0.0245 = 0.048
Therefore, we can be 95% confident that the true proportion of adults who support the law is between 0.60 – 0.048 = 0.552 and 0.60 + 0.048 = 0.648.
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