Final answer:
To calculate the chi-square value for the chicken cross data, apply the formula for chi-square analysis by comparing observed outcomes to expected ratios, as predicted by Mendelian genetics laws of independent assortment.
Step-by-step explanation:
Determining Chi-Square Value
To determine whether the data from the cross of chickens with gray and black feathers and spotted and solid patterns are consistent with expectations for independent assortment, a chi-square analysis is used. Independent assortment predicts that each pair of alleles segregates independently of the other pairs of alleles during gamete formation.
In the scenario provided, chickens that are heterozyous for both traits exhibit Mendelian genetics principles.
For a dihybrid cross (AaBb x AaBb), the expected phenotypic ratio is 9:3:3:1 according to Mendel's law of independent assortment.
To determine the chi-square value, you would first need to calculate the expected numbers for each phenotype based on the ratio of 9:3:3:1, then use the formula χ² = ∑ ((observed - expected)² / expected) for each phenotype category.
The sum of these values would provide the chi-square value to compare with a critical value from a chi-square distribution table at a certain degree of freedom to determine if the observed ratios are significantly different from the expected ratios.