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# Chapter 14: The Chi-Square Distribution ## 14.1 Facts About the Chi-Square Distribution ### Notation - $\chi^{2}$ = Greek letter chi (pronounced "kye") - $df$ = degrees of freedom ### Chi-Square Distribution - A distribution for: - Hypothesis testing - Confidence intervals ### Compar...

# Chapter 14: The Chi-Square Distribution ## 14.1 Facts About the Chi-Square Distribution ### Notation - $\chi^{2}$ = Greek letter chi (pronounced "kye") - $df$ = degrees of freedom ### Chi-Square Distribution - A distribution for: - Hypothesis testing - Confidence intervals ### Comparing | Normally distributed | Chi-Square distribution | | :------------------- | :----------------------- | | | | ### Looks Like - A chi-square distribution is a non-negative distribution. - Curve is non-symmetrical ### Similarities - The shape depends on df. - Different df's give different Chi-Square curves. ### Properties - Mean: $\mu = df$ - Standard deviation: $\sigma = \sqrt{2(df)}$ ### Example If $df$ = 10, then - $\mu = 10$ - $\sigma = \sqrt{2(10)} = 4.47$