A plant breeder crossed a homozygous purple-flowered, hairy-stemmed plant (genotype PPHH) with a homozygous white-flowered, smooth-stemmed plant (pphh). The purple flower allele (P) is dominant to white (p), and hairy stem allele (H) is dominant to smooth (h). The F1 plants were all purple-flowered and hairy-stemmed. The breeder then performed a test cross by crossing an F1 plant with a homozygous recessive plant (pphh). The following offspring were obtained:
| Phenotype | Number of offspring |
|---|---|
| Purple, hairy | 62 |
| White, smooth | 58 |
| Purple, smooth | 14 |
| White, hairy | 18 |
The chi-squared (χ²) formula is: χ² = Σ (O - E)² / E, where O = observed frequency, E = expected frequency.
Critical values of χ² at 5% significance level:
| Degrees of freedom | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Critical value | 3.84 | 5.99 | 7.82 | 9.49 | 11.07 |
Determine whether the genes for flower colour and stem hairiness are linked. Use the data and chi-squared test to support your answer.