Question 6.EX.4: Suppose that the data on educational achievement and employm...
Suppose that the data on educational achievement and employment status in Chapter 1 were obtained from a sample of 1002 people, as follows:
| Higher education | A-levels | Other qualification | No qualification | Total | |
| In work | 222 | 153 | 302 | 70 | 747 |
| Unemployed | 6 | 6 | 19 | 8 | 39 |
| Inactive | 26 | 37 | 84 | 69 | 216 |
| Total | 254 | 196 | 405 | 147 | 1002 |
Test whether there is an association between education and employment status, using the 5% significance level for the test.
The expected values are:
| Higher education | A levels | Other qualification | No qualification | Total | |
| In work | 189 | 146 | 302 | 110 | 747 |
| Unemployed | 10 | 8 | 16 | 6 | 39 |
| Inactive | 55 | 42 | 87 | 32 | 216 |
| Total | 254 | 196 | 405 | 147 | 1002 |
(These are calculated by multiplying row and column totals and dividing by the grand total, e.g. 189 = 747 × 254/1002.)
The test statistic is
5.6 + 0.3 + 0.0 + 14.3 + 1.5 + 0.3 + 0.7 + 0.9 + 15.1 + 0.7 + 0.1 + 43.9 = 83.5
This should be compared to a critical value of 12.59 (ν = (3 − 1) × (4 − 1) = 6) so the null is rejected.
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