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1) If the population is normal, then \( \dfrac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1} \).
2) The chi-square distribution is symmetric about its mean.
3) The degrees of freedom parameter changes the shape of the chi-square distribution.
4) A CI for \( \sigma^2 \) based on chi-square in a normal model uses df \( = n \).
5) For a chi-square test of independence, a common rule-of-thumb is expected counts ≳ 5 in most cells.
6) A chi-square random variable can take negative values.
7) For \( \chi^2_{\nu} \), the mean is \( \nu \) and the variance is \( 2\nu \).
8) In a GOF test, the usual contribution is \( \dfrac{(O-E)^2}{O} \).
9) Holding \( \alpha \) fixed, the upper-tail chi-square critical value generally decreases as df increases.
10) You can safely use chi-square variance procedures without normality assumptions.