= Solution
The displayed percentages use row denominators. The relevant comparison is therefore the <conditional probability> of each response within each recorded gender group, rather than the gender composition within a response category.
For the male group, $364/1042\approx34.93\%$ strongly agree and $286/1042\approx27.45\%$ agree. For the female group, the corresponding percentages are $225/1093\approx20.59\%$ and $243/1093\approx22.23\%$. Combining the two agreement categories gives
$$
\boxed{\widehat p_M=\frac{650}{1042}\approx62.38\%,\quad
\widehat p_F=\frac{468}{1093}\approx42.82\%,\quad
\widehat p_M-\widehat p_F\approx19.56\text{ percentage points}.}
$$
The female group has more neutral responses, $24.25\%$ versus $17.47\%$, and a higher combined disagreement percentage, $32.94\%$ versus $20.15\%$. Thus the observed distributions differ in more than a single cell.
The <Pearson chi-squared test> assesses the <null hypothesis> of <independence> in the complete $2\times5$ <contingency table>. Under that null, the <expected frequency> in a cell is its row total times its column total divided by 2,135. Recalculation gives
$$
X^2=\sum_{i,j}\frac{(O_{ij}-E_{ij})^2}{E_{ij}}\approx90.56953,\qquad
\nu=(2-1)(5-1)=4.
$$
The reported <p-value>, approximately $9.97\times10^{-19}$, gives very strong evidence against <independence> under the test's sampling assumptions. The minimum <expected frequency> is about $106.88$, so sparse expected cells are not a problem here. The test concerns the full five-category distribution, not just the combined agreement comparison.
<Cramér's V> summarizes the magnitude without imposing an ordering on the gender labels:
$$
V=\sqrt{\frac{90.56953}{2135\min(2-1,5-1)}}\approx0.206.
$$
The small <p-value> does not imply a nearly deterministic relationship. For example, the column-dependent <Goodman and Kruskal's lambda> is only about $0.026$: choosing the modal response separately within the two groups reduces prediction errors from 1,546 to 1,506, a relative reduction of $40/1546\approx2.59\%$.
The positive <Goodman and Kruskal's gamma> must be interpreted using the table's chosen ordering. The agreement categories run toward less willingness, and gender has no intrinsic ordinal direction. A sign attached to an arbitrary group coding cannot replace the substantive comparison of <conditional probabilities>.
The <NaN> displayed for the likelihood-ratio calculation is not a valid <p-value> and is not evidence of no association. The <Pearson chi-squared statistic> can be independently recomputed from the positive cell counts. None of these calculations identifies a <causal effect>; the table has not controlled for income or other possible <confounders>.
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