Confidence Interval for the Proportion
If a characteristic is present in a proportion of a population, p, the proportion of individuals with that characteristic, p', in the samples of size n is distributed according to:
The confidence interval for the proportion is:
q = 1 − p.
The maximum error is:
Example
In an electronic components factory, the proportion of defective final components is 20%. After a series of investments designed to improve performance, a random sample of 500 components found that 90 of them were defective. What level of confidence should be taken to accept that performance has not changed?
p = 0.2 1 − p =0.8 p'= 90/ 500 = 0.18
E = 0.2 - 0.18 = 0.02
P (1 - zα/2 <1.12) = 0.86861 - 0.8686 = 0.1314
0.8686 - 0.1314 = 0.737
Level of confidence: 73.72%
