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 σ². When the samples are normally distributed, the ratio s²(n-1)/σ² follows a χ²-distribution (pronounced: chi-square).

The upper tails of the distribution have been tabulated (or you may use the distribution calculator). χ²(α) depicts the area of α% in the upper tail of the χ² distribution, i.e. Prob( χ² > χ²(α)) = α. The shape of the χ²-distribution depends on the degrees of freedom n-1.