In a survey of 100 people classified by literacy and employment status, the observed frequencies are shown. Compute the chi-square statistic and state what it says about the two attributes.

| | Employed | Unemployed | Total |
|---|---|---|---|
| **Literate** | 30 | 20 | 50 |
| *

Question

In a survey of 100 people classified by literacy and employment status, the observed frequencies are shown. Compute the chi-square statistic and state what it says about the two attributes.

| | Employed | Unemployed | Total |
|---|---|---|---|
| **Literate** | 30 | 20 | 50 |
| **Illiterate** | 30 | 20 | 50 |
| **Total** | 60 | 40 | 100 |

Accepted Answer

**Step 1 — Compute the expected frequencies, $E_{ij} = R_i C_j / N$, $N = 100$.** Row totals both 50; column totals 60 (Employed), 40 (Unemployed).
$$E(	ext{Literate, Employed}) = \dfrac{50 	imes 60}{100} = 30, \qquad E(	ext{Literate, Unemployed}) = \dfrac{50 	imes 40}{100} = 20$$
$$E(	ext{Illiterate, Employed}) = \dfrac{50 	imes 60}{100} = 30, \qquad E(	ext{Illiterate, Unemployed}) = \dfrac{50 	imes 40}{100} = 20$$

**Step 2 — Compare observed with expected.**

| Cell | $O$ | $E$ | $O-E$ | $(O-E)^2/E$ |
|---|---|---|---|---|
| Literate, Employed | 30 | 30 | 0 | 0 |
| Literate, Unemployed | 20 | 20 | 0 | 0 |
| Illiterate, Employed | 30 | 30 | 0 | 0 |
| Illiterate, Unemployed | 20 | 20 | 0 | 0 |
| **Total** | | | | **0** |

**Step 3 — Sum.**
$$\chi^2 = 0 + 0 + 0 + 0 = 0$$ …

Cell	$O$	$E$	$O-E$
Literate, Employed	30	30	0
Literate, Unemployed	20	20	0
Illiterate, Employed	30	30	0
Illiterate, Unemployed	20	20	0
Total

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