7 In a standard model from genetic theory, the ratios of types \(a , b , c\) and \(d\) of a characteristic from a genetic cross are predicted to be 9:3:3:1. Andrei collects 120 specimens from such a cross, and the numbers corresponding to each type of the characteristic are given in the table.
| Type | \(a\) | \(b\) | \(c\) | \(d\) |
| Frequency | 51 | 33 | 30 | 6 |
Andrei tests, at the 1\% significance level, whether the observed frequencies are consistent with the standard model.
- State appropriate hypotheses for the test.
- Carry out the test.
- State with a reason which one of the frequencies is least consistent with the standard model.
- Suggest a different, improved model by changing exactly two of the ratio values.