Introduction to Statistical Confidence Intervals
In statistics, a confidence interval (CI) is a range of values, derived from sample data, that is likely to contain the value of an unknown population parameter. It is expressed with a specific confidence level (such as 90%, 95%, or 99%), which represents the proportion of intervals that would contain the parameter if the population was sampled repeatedly. Confidence intervals are a key element of inferential statistics, offering more information than a single point estimate (like a sample mean) by quantifying the estimate's precision and uncertainty.
Confidence intervals are computed differently depending on the parameter of interest (means vs. proportions) and the availability of population parameters. When constructing an interval for a mean with a known population standard deviation, we use the Z-distribution. If the population standard deviation is unknown, we use the Student's t-distribution. For binary categorical variables, we construct a confidence interval for a proportion using normal approximations.
This calculator constructs confidence intervals for both means and proportions. By inputting the sample size, sample mean or count, standard deviation, and desired confidence level, the solver computes critical values ($Z^*$ or $t^*$), standard errors, the margin of error, and the final lower and upper confidence limits.