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95% Confidence Interval Formula:
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A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. It provides an estimate of the precision and uncertainty associated with a sample statistic.
The calculator uses the standard formula for 95% confidence interval:
Where:
Explanation: The formula calculates the margin of error by multiplying the standard error (SD/√n) by the z-score for 95% confidence, then adds and subtracts this from the sample mean.
Details: Confidence intervals provide more information than point estimates alone. They indicate the precision of an estimate and the uncertainty around it, which is crucial for statistical inference and decision-making.
Tips: Enter the sample mean, standard deviation, and sample size. All values must be valid (n > 0, SD ≥ 0). The calculator will compute the 95% confidence interval.
Q1: Why use 1.96 in the formula?
A: 1.96 is the z-score that corresponds to 95% confidence level in a standard normal distribution, capturing 95% of the area under the curve.
Q2: When should I use a t-score instead of a z-score?
A: Use a t-score when sample size is small (n < 30) and population standard deviation is unknown. For larger samples, the z-score is appropriate.
Q3: What does a narrower confidence interval indicate?
A: A narrower interval indicates more precise estimate of the population parameter, typically resulting from larger sample sizes or smaller variability.
Q4: Can confidence intervals be used for proportions?
A: Yes, but the formula differs. For proportions, the formula is: \( p \pm 1.96 \times \sqrt{\frac{p(1-p)}{n}} \).
Q5: What if my data is not normally distributed?
A: For non-normal distributions, consider using bootstrapping methods or transformations to approximate normality before calculating confidence intervals.