Konfidenzintervall Rechner

Confidence interval is a range of values within which the true population value lies with a certain probability. A 95% confidence interval means that if the experiment were repeated many times, the true population mean would fall within the calculated interval 95% of the time.

Margin of error is half the width of the confidence interval, calculated as Z times the standard error. It depends on the confidence level (higher level = wider interval) and sample size (larger sample = narrower interval). Z = 1.96 for 95% confidence is standard.

Confidence level: Typical levels are 90%, 95%, and 99%. The 95% level is most common in scientific research. A higher confidence level gives a wider interval but more certainty. The choice depends on the precision-certainty tradeoff.

Sample size and margin of error: To halve the margin of error, we need to quadruple the sample size. Formula: n = (Z × σ / E)² where E is the desired margin of error. To get margin of 0.5 with standard deviation of 5, we need n = (1.96 × 5 / 0.5)² = 384 observations.

Interpretation: A confidence interval does not mean the true value has a 95% chance of being in that specific interval. It means that 95% of intervals constructed from different samples contain the true value. A single interval either contains it or does not.