$21\mathrm{.}23$ Mendel$$s second law. Mendel formulated the law of independent assortment as his second law of inheritance. It involves two genes independently segregated during reproduction, each independently determining one aspect of the phenotype. In one experiment, Mendel crossed pea plants producing yellow, round seeds with pea plants producing green, wrinkled seeds. The first generation resulted in only plants producing yellow, round seeds. Self$-$crossing of the F$1$ plants yielded the following phenotypes in F$2$: Phenotype Yellow, round Yellow, wrinkled Green, round Green, wrinkled Counts $31510110832$ Assuming two independent genes, each with a dominant allele and a recessive allele, we would expect to find a $9$:$3$:$3$:$1$ phenotypic ratio. Are the conditions for a chi$-$square goodness$-$of$-$fit test satisfied? What are the null and alternative hypotheses for this test? What are the expected counts under the null hypothesis? The chi$-$square statistic for this test is $.$ Obtain the test P$-$value. What can you conclude? Do the data agree with Mendel$$s second law of genetic inheritance?