Margin of Error
Suppose you are a pollster for a major political organization and you want to say with 99.9% certainty that the majority of the country disapproves of the current administration, but that you don't have very much time.
So you conduct a study with respondents. of them say they do not approve. This seems like great news, that of the sample does not approve. Even if these are a truly random sample of the population, what's your sampling error rate? What's your margin of error on a confidence interval?
Express your answer as a decimal. For instance, would be
The answer is 0.213.
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1 solution
Relevant wiki: Sampling (Statistics)
Margin of error is calculated using the equation: z n p ( 1 − p ) .
Where z is the z-score for the study's confidence interval , sometimes expressed as z ∗ , or the critical value. p is the portion of the sample who has the factor you're testing for, and n is the total sample population.
For a 9 9 . 9 % confidence interval, the z-score goes up to 3 . 2 9 , so the formula for this scenario works out to: 3 . 2 9 5 0 . 7 0 ( . 3 0 ) = . 2 1 3 = 2 1 . 3 % .
This is a very high error rate, and could mean that a representative sample of the US population actually has 2 4 . 4 people out of 5 0 who disapprove of the current administration, a vastly different conclusion (roughly 5 0 − 5 0 ), or that 4 5 . 7 people out of 5 0 disapprove, an even more extreme conclusion.
This is why honest pollsters conduct studies with large sample sizes and report lower confidence intervals.