Answer
$X^2_0\lt X_α^2$: null hypothesis is not rejected.
There is not enough evidence to conclude that the proportions are different for each category.
Work Step by Step
$H_0:$ the proportions are equal for each category
versus
$H_1:$ the proportions are different for each category
In MINITAB, enter the given values:
1-C1 = 204, 1-C2 = 199, 1-C3 = 214
2-C1 = 96, 2-C2 = 121, 2-C3 = 98
Select Stat -> Tables -> Chi-Square Test for Association
Select "Summarized data in a two-way table"
In columns containing the table enter: C1 C2 C3
Click OK.
$X^2_0=3.533$
$r=2$, $c=3$.
So, $d.f.=(r−1)(c−1)=2$
$X_α^2=X_{0.01}^2=9.210$
(According to Table VII, for d.f. = 2 and area to the right of critical value = 0.01)
Since $X^2_0\lt X_α^2$, we do not reject the null hypothesis.
Also, P-value $=0.171\gtα$
