# Ch 11.1 Chi-square Distribution

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**Ch 11.1 Facts about Chi-square distribution**

Notation for chi-square distribution is χ^{2} . It is a distribution with degree of freedom (df = n -1).

Characteristic of chi-square distribution.

i) Shape of the distribution is right skew,

non-symmetrical. There is a different chi-square curve for each df. When df > 90, the chi-square curve approximates the normal distribution.

ii) mean μ = df (n-1), σ = \( 2 \sqrt{df} \). The mean is located just right of the peak.

iii) = sum of (n-1) independent, standard normal variable. χ^{2} is always positive.

Chi-square distribution calculator:

http://onlinestatbook.com/2/calculators/chi_square_prob.html

The calculator can be used to find area to the right of a chi-square value P( χ^{2} > a)

Ex. Find probability that χ^{2} is greater than 31 when

df = 10.

Enter chi-square = 31, df = 10, calculate.