There are many times when a proportion from a population is required. For example, the proportion of people who may vote for a particular candidate in an election or the percentage of people watching a particular TV channel.
To estimate π a proportion from a population, the proportion from a sample, p, can be used as a point estimate of π
As with estimating the mean, a range of values with some level of probability or confidence that the population parameters will lie within this range is a better way to estimate the population proportion.
This range of values is called a confidence interval for proportions.
Degree of Confidence
The degree of confidence is given as a percentage probability changed into a zscore, using the standard normal distribution tables. Check out where the zscores are found in the tables for the following degrees of confidence.
Any degree of confidence can be found in this manner. e.g. For an 80% level of confidence look up 0.40 in the tables.
Confidence Intervals for Proportions
The confidence interval, based on the Central Limit Theorem, for the population proportion π is given by:
p ± z.

Where π is the population proportion. As π is often unknown, p the sample proportion can be used instead.
The value of z will depend upon the degree of confidence required. The z values for 90, 95 and 99% are shown above.
is called the standard error of the proportion.
In opinion polls z. is often called the margin of error.
Example
In a survey before an election, a poll (sample) was taken of 300 potential voters. 120 said they would vote for Candidate A. Calculate a 95% confidence interval for the proportion of voters who would vote for Candidate A in the election.
From the poll p = 120 / 300 = 0.4.
The 95% confidence interval is:
p ± z.
= 0.4 ± 1.96
=0.4 ± 0.0554
= (0.3446, 0.4554)
The 95% confidence interval for π is ( (0.3446, 0.4554) or between 34.46% and 45.54%
This is sometimes written 0.3446 < π < 0.4554
Note The margin of error for the poll is 0.0554 or 5.54%
Meaning of Confidence Intervals
The answer in the example above means that 95% of such confidence intervals will contain the population proportion.