5. Lily is interested in the relationship between the way in which students learned Welsh and their attitude towards the Welsh language.
Students were categorised as having learned Welsh in one of three ways:
- from one Welsh-speaking parent/carer at home,
- from two Welsh-speaking parents/carers at home,
- at school only, for those with no Welsh-speaking parents/carers at home.
The students were asked to rate their attitude towards the Welsh language from 'Very negative' to 'Very positive'.
The following data for a random sample of 253 students were collected as part of a project.
| Learned Welsh | |
| Attitude | From two parents/carers | From one parent/carer | At school only | Total |
| Very negative | 2 | 14 | 30 | 46 |
| Slightly negative | 4 | 20 | 21 | 45 |
| Neutral | 12 | 17 | 8 | 37 |
| Slightly positive | 21 | 19 | 11 | 51 |
| Very positive | 25 | 21 | 28 | 74 |
| Total | 64 | 91 | 98 | 253 |
Lily intends to carry out a chi-squared test for independence at the \(5 \%\) level. She produces the following tables which are incomplete.
| Expected Frequencies | Learned Welsh |
| Attitude | From two parents/carers | From one parent/carer | At school only |
| Very negative | 11.64 | 16.55 | 17.82 |
| Slightly negative | 11.38 | 16.19 | 17.43 |
| Neutral | 9.36 | 13.31 | 14.33 |
| Slightly positive | 12.90 | 18.34 | 19.75 |
| Very positive | F | 26.62 | 28.66 |
| Chi-Squared Contributions | Learned Welsh |
| Attitude | From two parents/carers | From one parent/carer | At school only |
| Very negative | 7.98 | 0.39 | 8.33 |
| Slightly negative | \(4 \cdot 79\) | 0.90 | 0.73 |
| Neutral | \(0 \cdot 74\) | 1.02 | G |
| Slightly positive | 5.08 | 0.02 | 3.88 |
| Very positive | 2.11 | 1.19 | 0.02 |
| Total | 20.70 | 3.52 | H |
- Calculate the values of \(F , G\) and \(H\).
- Carry out Lily's chi-squared test for independence at the \(5 \%\) level.
- By referring to the figures in the tables on pages 16 and 17, give two comments on the relationship between the way students learned Welsh and their attitude towards the Welsh language.