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Section 11.1 The Chi-square Distribution
Figure 11.1.1. Chi-square Distribution (Made in GeoGebra by Chris Rosenthal)
Investigation 11.1.1.
(a)
The \(\chi^2\) distribution curves are not symmetric, but instead are .....positively skewed
-
negatively skewed
-
(b)
As the degrees of freedom increases, the skewness .....
decreases
-
increases
-
stays the same
-
(c)
(d)
We can use Table 8 in Appendix A of your book to find critical \(\chi^2\) values. The notation for these is \(\chi^2_{\alpha,df}\text{.}\)
Find the desired significance level, \(\alpha\text{,}\) across the top of the table.
Locate \(df\) along the left of the table.
We can also find critical \(\chi^2\)-values using the Excel command
\begin{equation*}
CHISQ.INV.RT
\end{equation*}
Exercise 11.1.2.
Find the following critical \(\chi^2\)-values:
(a)
\(\chi^2_{0.10,5}\)
(b)
\(\chi^2_{0.975,24}\)
(c)
\(\chi^2_{0.01,19}\)
(d)
\(\chi^2_{0.90,10}\)
