Confidence Interval for the Variance
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Example: a machine fills 500 ml bottles. In 25 bottles measured, the standard deviation was 4 ml. Between what values should the machine's standard deviation lie, with 95% confidence? Change the values to work out your own case.
Step by step
What each term means
- Interval for the Variance
- The range of plausible values for the population variance σ². Taking the square root of the bounds gives the interval for the standard deviation σ.
- Sum of Squares ((n − 1)s²)
- The sample's total variation. With normal data, (n − 1)s²/σ² follows a chi-square with n − 1 degrees of freedom — that is where the interval comes from.
- Upper Critical Value
- The chi-square value that leaves α/2 above it. Being in the denominator, it gives the lower bound of the interval.
- Lower Critical Value
- The one that leaves α/2 below it, and gives the upper bound. Since the chi-square is skewed, the interval isn't centred on s².
When to use it, assumptions and alternatives: the chi-square test for variance in the statistical tests catalog.