AP4.40 The table provides data on the political affiliation and opinion about the death penalty of 850 randomly selected voters from a congressional district.

a.$\frac{299}{494}\ne \frac{98}{356}$

b.$\frac{299}{494}\ne \frac{397}{850}$

c.$\frac{494}{850}\ne \frac{299}{397}$

d.$\frac{494}{850}\ne \frac{397}{850}$

e.$\frac{\left(397\right)\left(494\right)}{850}\ne 299$

To determine that which of the following does not support the conclusion that being a Republican and favoring the death penalty are not independent.

If the proportion of republicans among those who prefer the death penalty is the same as the proportion of Republicans in the overall sample, "Republican" and "Favoring" the death penalty are independent.
Highlight that $299$Republicans support the death penalty, whereas $494$ persons in the sample support the death penalty.
As a result, the percentage of republicans who support the death penalty is:
$\frac{299}{494}=0.6053$
While there are $850$people in the sample, $397$ of them are republicans.
As a result, the percentage of republicans in the sample is as follows:
$\frac{397}{850}=0.4671$
And the two proportions are not equal.

Hence,
$\frac{299}{494}\ne \frac{397}{850}$
As a result, option (b) is the correct answer.