How to calculate confidence interval for means with unknown standard deviation using the Student t distribution. Needs Apache Commons Math library.

ConfidenceIntervalApp.java

import org.apache.commons.math3.distribution.TDistribution;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.stat.descriptive.SummaryStatistics;

public class ConfidenceIntervalApp {

    public static void main(String args[]) {
        // data we want to evaluate: average height of 30 one year old male and female toddlers
        // interestingly, at this age height is not bimodal yet
        double data[] = new double[] { 63.5, 81.3, 88.9, 63.5, 76.2, 67.3, 66.0, 64.8, 74.9, 81.3, 76.2, 72.4, 76.2, 81.3, 71.1, 80.0, 73.7, 74.9, 76.2, 86.4, 73.7, 81.3, 68.6, 71.1, 83.8, 71.1, 68.6, 81.3, 73.7, 74.9 };
        // Build summary statistics of the dataset "data"
        SummaryStatistics stats = new SummaryStatistics();
        for (double val : data) {
            stats.addValue(val);
        }

        // Calculate 95% confidence interval
        double ci = calcMeanCI(stats, 0.95);
        System.out.println(String.format("Mean: %f", stats.getMean()));
        double lower = stats.getMean() - ci;
        double upper = stats.getMean() + ci;
        System.out.println(String.format("Confidence Interval 95%%: %f, %f", lower, upper));
    }

    private static double calcMeanCI(SummaryStatistics stats, double level) {
        try {
            // Create T Distribution with N-1 degrees of freedom
            TDistribution tDist = new TDistribution(stats.getN() - 1);
            // Calculate critical value
            double critVal = tDist.inverseCumulativeProbability(1.0 - (1 - level) / 2);
            // Calculate confidence interval
            return critVal * stats.getStandardDeviation() / Math.sqrt(stats.getN());
        } catch (MathIllegalArgumentException e) {
            return Double.NaN;
        }
    }

}