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95% Confidence Interval Formula:
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A confidence interval (CI) is a range of values that's likely to include a population parameter with a certain degree of confidence (typically 95%). It provides an estimated range of values which is likely to include an unknown population parameter.
The calculator uses the following formula:
Where:
Explanation: The confidence interval is calculated by taking the mean and adding/subtracting the margin of error, which is the product of the z-score and standard error.
Details: Confidence intervals provide more information than point estimates alone. They indicate the precision of the estimate and the uncertainty around it. A narrower interval suggests more precise estimates.
Tips: Enter the mean value, standard error, and z-score (default is 1.96 for 95% CI). The calculator will compute the lower and upper bounds of the confidence interval.
Q1: Why use 1.96 for 95% confidence intervals?
A: 1.96 is the z-score that corresponds to the 97.5th percentile of the standard normal distribution, leaving 2.5% in each tail for a total of 5% outside the 95% confidence interval.
Q2: What's the difference between standard deviation and standard error?
A: Standard deviation measures variability in the data, while standard error measures the precision of the sample mean as an estimate of the population mean (SE = SD/√n).
Q3: When would I use a different z-score?
A: For different confidence levels: 1.645 for 90% CI, 2.576 for 99% CI. Use t-scores instead of z-scores for small samples (typically n < 30).
Q4: Can I calculate CI for proportions?
A: Yes, the formula is similar but uses the standard error of the proportion instead of the mean.
Q5: What does "95% confidence" actually mean?
A: If we repeated the study many times, 95% of the calculated confidence intervals would contain the true population parameter.