Answer
$X^2_0\lt X_α^2$: null hypothesis is not rejected.
There is not enough evidence to conclude that the proportion of cardiovascular events in each treatment group is different.
$X_0^2=2.061$
Work Step by Step
$E(cardiovascular~event~and~aspirin)=\frac{(row_1~total)(collumn_1~total)}{table~total}=\frac{999\times19934}{39876}=499.4$
$E(cardiovascular~event~and~placebo)=\frac{(row_1~total)(collumn_2~total)}{table~total}=\frac{999\times19942}{39876}=499.6$
$E(no~cardiovascular~event~and~aspirin)=\frac{(row_2~total)(collumn_1~total)}{table~total}=\frac{38877\times19934}{39876}=19434.6$
$E(no~cardiovascular~event~and~placebo)=\frac{(row_2~total)(collumn_2~total)}{table~total}=\frac{38877\times19942}{39876}=19442.4$
$X_0^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(477-499.4)^2}{499.4}+\frac{(522-499.6)^2}{499.6}+\frac{(19457-19434.6)^2}{19434.6}+\frac{(19420-19442.4)^2}{19442.4}=2.061$
$r=2$, $c=2$.
So, $d.f.=(r−1)(c−1)=1$
$X_α^2=X_{0.05}^2=3.841$
(According to Table VII, for d.f. = 1 and area to the right of critical value = 0.05)
Since $X^2_0\lt X_α^2$, we do not reject the null hypothesis.
