# Hypothesis Testing - Statistical Test of Variance - Theory & Examples

### Statistical Hypothesis: Testing Variance -- Population

Population distribution:

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### Statistical Hypothesis: Testing Variance -- Sample

Sample statistics:

Sample distribution:

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Table overview:

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Definition

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Property 1

Property 2

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Rule of thumb

Example

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### Statistical Hypothesis: Testing Variance -- Distribution of Sample Variance

Proof

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From a random sample, with sample size n and drawn from a population following a normal distribution and given mean and standard deviation, the sample variance can be estimated as described in the following cases.

Estimation - Case 1: mean is unknown

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Estimation - Case 1: mean is known

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### Statistical Hypothesis: Testing Variance -- Summary

Estimation of variance - distribution of test statistic - degrees of freedom

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### Statistical Hypothesis: Testing Variance -- Example 4: Confidence intervals for Population Variance

#### Conclusion

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