= Solution
\b[The displayed age groups have fairly similar employment proportions, with no coherent <monotone> age trend. The printed test reports no evidence against age–employment <independence>; recomputing from the five visible rows reaches the same qualitative conclusion. Their totals and several auxiliary fields nevertheless do not represent one consistent table.]
Each row <percentage> estimates an employment proportion \i[within that age group]. For example, $105/182=57.69\%$ of the youngest displayed group are employed. The employed proportions in the next four rows are $61.57\%$, $62.26\%$, $56.69\%$ and $57.23\%$. The largest displayed proportion is in the 45–54 group and the smallest in the 55–64 group, a difference of about $5.57$ <percentage points>. These are conditional <percentages>, not the age distribution of employed people. The sequence rises and then falls; there is no simple increasing or decreasing pattern.
The <null hypothesis> for a <Pearson chi-squared test of independence> is that the joint category <probabilities> factor into their age and employment marginals. Its <expected frequencies> are $E_{ij}=n_{i+}n_{+j}/n$, and its <test statistic> adds the standardized squared count discrepancies, $X^2=\sum_{ij}(O_{ij}-E_{ij})^2/E_{ij}$. For a complete $r\times c$ <contingency table> with positive margins, the large-sample reference <chi-squared distribution> has $(r-1)(c-1)$ <statistical degrees of freedom>. <Independent> observations and an appropriate sampling scheme are essential; adequate <expected counts> make the approximation more plausible.<Pearson's Chi-squared Test for Count Data in the R documentation>[Details: independence null, asymptotic reference distribution and observed/expected counts]{ref}
Reading only the printed test block, $X^2=4.83463$, $5$ <statistical degrees of freedom> and $p\approx0.4364$ are mutually compatible. The printed <likelihood-ratio test> gives nearly the same <p-value>, about $0.435$. At a prechosen 5% <significance level> neither rejects <independence>. This is a failure to find evidence, not proof of equal employment <probabilities> at every age. The printed <Cramér's V> around $0.049$ suggests a small sample association; the <contingency coefficient> around $0.048$ has the same broad message. The <generalized phi coefficient> is an unsigned chi-squared magnitude here, not evidence for a positive age trend. A small association magnitude and a large <p-value> answer different questions.
But only a $5\times2$ table is actually visible. Those rows total $1730$, with employment column sums $698$ and $1032$, rather than the printed $2053$ with columns $837$ and $1216$. Computing solely from the five visible rows gives
$$
X^2\approx4.034032,\qquad \nu=4,\qquad p\approx0.40142,\qquad V\approx0.04829.
$$
Its <likelihood-ratio test statistic> is about $4.03243$, again with $4$ <statistical degrees of freedom>. The smallest count-based <expected frequency> is about $73.43$, comfortably large for this ordinary approximation, but different from the printed minimum $74.20068$. These figures are a labelled analysis of the \i[visible subset], not a repaired full dataset. An unprinted sixth age row might explain some intended metadata, but neither its label nor a uniquely justified reconstruction is supplied. The oldest printed label also conflicts with Figures 1 and 8.
The ordinal measures look for an ordered tendency. <Goodman and Kruskal's gamma> compares <concordant pairs> with <discordant pairs> among pairs untied on both variables. The printed negative gamma, <Somers' D>, <Kendall's tau-b> and <Stuart's tau-c> therefore suggest, at most, a very weak tendency toward lower employment at higher age categories under the specified ordering. Their precise magnitudes are not reliable here. The ordinary <unordered-pair partition for ordinal data> fails for the printed pair counts, even when compared with the printed $2053$ cases. On the five visible rows the respective count-based values are about $-0.0356$, $-0.0172$ for employment conditional on age, $-0.0218$ and $-0.0266$. None gives a substantial <monotone> pattern; a near-zero ordinal measure would not exclude a nonmonotone relationship in general.
<Goodman and Kruskal's lambda> is zero in both predictive directions on the visible table: knowing age does not improve the number of correct predictions made by always choosing the most common employment category, and knowing employment does not improve modal age-category prediction. Zero modal-prediction improvement does not mean every category distribution is identical. \b[Both the reported test block and the separately recomputed visible-table test fail to reject <independence>; neither justifies asserting no association, a causal age effect, or a coherent full-sample calculation from the contradictory printout.]
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