91Ó°ÊÓ

The table with observed values:

$\begin{array}{|cccccccc|}\hline & \text{Stra}& \text{Choco}& \text{Van}& \text{R R}& \text{M C C}& \text{Pist}& \text{Total}\\ \text{West}& 12& 21& 22& 19& 15& 8& 97\\ \text{Midwest}& 10& 32& 22& 11& 15& 6& 96\\ \text{East}& 8& 31& 27& 8& 15& 7& 96\\ \text{South}& 15& 28& 30& 8& 15& 6& 102\\ \text{Total}& 45& 112& 101& 46& 60& 27& 391\\ \hline\end{array}$

The table with expected values:

$\begin{array}{|cccccccc|}\hline & \text{Stra}& \text{Choco}& \text{Van}& \text{R R}& \text{M C C}& \text{Pist}& \text{Total}\\ \text{West}& 11.16& 27.79& 25.056& 11.41& 14.88& 6.7& 97\\ \text{Midwest}& 11.05& 27.5& 24.8& 11.29& 14.73& 6.63& 96\\ \text{East}& 11.05& 27.5& 24.8& 11.29& 14.73& 6.63& 96\\ \text{South}& 11.74& 29.22& 26.35& 12& 15.65& 7.04& 102\\ \text{Total}& 45& 112& 101& 46& 60& 27& 391\\ \hline\end{array}$

We want to test the following hypotheses:

$H_0$: Geographic location is independent of favorite ice cream flavors

$H_1$: Geographic location depends on favorite ice cream flavors

Since there are $4$regions and $6$flavors, the number of degrees of freedom is

$(4-1)(6-1)=15$

We are using ${\mathrm{χ}}^2$distribution. The test statistic is given by:

${\mathrm{χ}}^2=\underset{i=1}{\overset{4}{∑}}\underset{j=1}{\overset{6}{∑}}\frac{{\left(O{b}_{i,j}-E{x}_{i,j}\right)}^2}{E{x}_{i,j}}=14.06317$

Using the applet for ${\mathrm{χ}}^2$distribution, we get that $p$-value is $0.52074$:

Chi-Square Distribution

$X~{\mathrm{χ}}_{\left(df\right)}^2$