In a species of beetle, wing length and antenna colour are controlled by two autosomal genes. Long wings (L) are dominant over short wings (l), and black antennae (B) are dominant over brown antennae (b). A test cross was carried out: a dihybrid beetle (LlBb) was crossed with a double recessive beetle (llbb). The offspring were counted and their phenotypes recorded.
| Phenotype | Number |
|---|---|
| Long wings, black antennae | 312 |
| Short wings, brown antennae | 288 |
| Long wings, brown antennae | 105 |
| Short wings, black antennae | 95 |
Using a chi-squared test, determine whether these data provide evidence that the two genes are linked. Use the formula and a significance level of 5%. The critical value for the chi-squared distribution with 3 degrees of freedom at the 5% level is 7.82.