Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

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.