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Confidence Interval Formula:
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A confidence interval (CI) is a range of values that's likely to include a population value with a certain degree of confidence. It's calculated from the sample data and provides an estimated range of values which is likely to include an unknown population parameter.
The calculator uses the standard confidence interval formula:
Where:
Explanation: The width of the confidence interval depends on the standard error and the confidence level (determined by the z-score).
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.
Tips: Enter the sample mean, standard error, and select the appropriate z-score for your desired confidence level (or enter a custom z-score). The calculator will compute the margin of error and the confidence interval bounds.
Q1: What's the difference between 90%, 95%, and 99% CIs?
A: Higher confidence levels produce wider intervals. A 95% CI means if we repeated the study many times, 95% of the CIs would contain the true population mean.
Q2: When should I use a t-score instead of a z-score?
A: Use t-scores when sample sizes are small (typically n < 30) and population standard deviation is unknown. For larger samples, z-scores are appropriate.
Q3: How is standard error calculated?
A: Standard error is the standard deviation divided by the square root of the sample size (SE = σ/√n).
Q4: Can I use this for proportions?
A: The same formula structure applies, but the standard error calculation differs for proportions.
Q5: What does "±" mean in the results?
A: It represents the margin of error - the amount added and subtracted from the mean to create the interval.