A Geneticist Is Investigating the Inheritance of Two Autosomal Recessive

A geneticist is investigating the inheritance of two autosomal recessive genes in mice, one for obesity (LEP) and another for autism (oprm1). The table below provides the number of offspring observed, for each phenotype, when dihybrid mice are testcrossed: $$\begin{array} { | l | c | l | l | l | l | } \hline \text { Phenotype } & \text { Observed(O) } & \text { Expected } ( \mathrm { E } ) & \mathrm { O } - \mathrm { E } & ( \mathrm { O } - \mathrm { E } ) 2 & ( \mathrm { O } - \mathrm { E } ) 2 / \mathrm { E } \\\hline \text { wild- type } & 88 & & & & \\\hline \text { obese } & 68 & & & & \\\hline \text { autistic } & 64 & & & & \\\hline \text { obese, autistic } & 80 & & & & \\\hline & & & & & \sum ( \mathrm { O } - \mathrm { E } ) ^ { 2 } / \mathrm { E } = \\\hline\end{array}$$ Fill in the table above and determine:
a. the chi- square (χ²) value (to the nearest hundredth) for the chance hypothesis that the two genes assort independently
b. the degrees of freedom
c. whether or not you would reject your chance hypothesis that the two genes assort independently, based on approximate P value, and the justification for why