In a species of insect, body colour (grey or black) and wing shape (normal or vestigial) are controlled by two autosomal genes. A grey-bodied, normal-winged insect that is heterozygous for both genes is test-crossed with a black-bodied, vestigial-winged insect. The offspring phenotypes and numbers are shown in the table.
| Phenotype | Number of offspring |
|---|---|
| Grey, normal | 305 |
| Grey, vestigial | 115 |
| Black, normal | 120 |
| Black, vestigial | 310 |
Determine whether the two genes are linked. Use a chi-squared test at the 5% significance level. The critical value for 3 degrees of freedom is 7.82. Show all your working.