We use the chi-square distribution when making inferences about a single population variance.
Short Description of Chi-Square Distribution
The continuous probability distribution known as the chi-square distribution. The number of degrees of freedom (k) a chi-square distribution has determines its shape. This type of sampling distribution has a variance of 2k and a mean equal to its number of degrees of freedom (k). The range is of a chi-square distribution is from 0 to ∞.
Variance plays a key role in the analysis of risk and uncertainty. The sample variance, an unbiased estimator of population variance, is expressed by the following formula of core statistic for a sample size 'n' and Y' as the sample mean:
S² = ∑(Yₓ - Y') / (n-1)
The formula, (n-1)S² / σ² has the central chi-square distribution as χ²ₙ₋₁. Here (n-1) represents the degrees of freedom.
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