Ximpledu

Margin of Error

See how to find the margin of error
(+ binomial confidence interval).
1 example and its solution.

Binomial Confidence Interval

Confidence Interval: Binomial Distribution to Normal Approximation

p̂ - Zp̂q̂n p ≤ p̂ + Zp̂q̂n
p̂: Probability of 'want' in the sample
(p̂ is read as [p hat].)
q̂: 1 - p̂
Probability of 'not want' in the sample
Z: Z-score
n: Sample size

In reality, it's hard to find the probability of 'want' in the population p.
(It takes so much time and effort.)
So, instead of finding the exact value of p,
we guess that p is in this confidence interval.

Margin of Error

Formula

(margin of error) = Zp̂q̂n

Example

A poll was taken of a random sample of 256 people.
64% of the people favored the candidate A.
For a 95% confidence level, find the margin of error.
(Assume P(-1.96 ≤ Z ≤ 1.96) = 0.95.)
Solution