Confidence Interval for Proportions

This calculator will determine the confidence interval for a chosen confidence level given a study’s sample size and survey result. This calculator tests proportions. To test a mean, use the Confidence Interval for Means calculator.

 

Step 1 Select desired confidence level:   %  
Step 2 Enter sample size:
Enter number of interviews completed
   
Step 3 Enter observed survey result:
Enter as a frequency or percent of the number of interviews.
 

or
frequency

%
percent

RESULT Confidence interval:
Click the Calculate button
  Range for true population mean:      to   
  Reset Form Calculate Form

What the results mean

When you are interviewing a sample of respondents drawn from a population, the percentage value (proportion) you obtain at a certain question may be different from the percentage value you would obtain if all members of the population where interviewed (true population proportion). There is some likelihood, called the confidence level, that the true population percentage falls within a particular range, called the confidence interval, around the proportion value you obtained from your sample.

For example, if you interview 500 people, and find that 75% of them answer a question in a particular way and you desire your confidence level to be 95%, the corresponding confidence interval is 3.8%. That is to say that you are 95% certain that the true population proportion falls into the range from 71.2% to 78.8%.

More information

Step 1: Confidence Level

The value chosen in Step 1 determines the confidence level of your results. It tells you how often the true percentage of the population would fall within the confidence interval of results obtained in your survey. For most marketing research studies, a confidence level of 95% is used.

Confidence level is related to the level of significance (α ). A 95% Confidence level corresponds to α = .05. If the Level of significance (α) = .05, that means that there is one chance in twenty that the true population proportion falls outside the range given.

Step 2: Sample Size

This is the number of respondents who answered the question.

Step 3: Enter Observed Study Result

This is the frequency or percentage of respondents in the sample who answered the question in the particular way you are interested in testing. You can enter either the frequency of respondents who answered in this manner or the percentage. The other result will calculate automatically. Given a choice, it is more accurate to enter the frequency response.

Assumptions

This calculation assumes you are testing the 2-tail hypothesis that the true population value is different (higher or lower) than the value observed in the subset of the population interviewed.

It is also assumed that your sample represents a random sample of the relevant population.

 
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