One Sample Chi-Square-Test

Certain problems require not only that the mean conforms to some restrictions, but also that the variance is within certain limits, i.e. not larger than a given value. So we have to compare the estimated sample variance  with the hypothetical variance s². When the samples are normally distributed, the ratio s²(n-1)/s² follows a -distribution (pronounced: chi-square).

The upper tails of the distribution have been tabulated (or you may use the distribution calculator). (a) depicts the area of a% in the upper tail of the  distribution, i.e. Prob(  > (a )) = a . The shape of the -distribution depends on the degrees of freedom n-1.