Question

You are studying a gene with two alleles, h and h, in a specific population. After determining the genotypes of all the individuals in the population, you calculate the observed and expected numbers of individuals for the three genotypes as follows:

Observed individuals: hh - 87; hh - 145; hh - 68.
Expected individuals: hh - 75; hh - 150; hh - 75.

What is the chi-square value calculated based on these observations?

a. 2.74
b. 0.73
c. 218
d. 2.55

Answer 1

The correct answer is option a.The correct chi-square value calculated from the provided observed and expected genotype numbers is 2.74, which matches option (a). This value is derived using the chi-square test formula to assess the deviation from Hardy-Weinberg equilibrium expectations.

Step-by-step explanation:

The student is asking for the chi-square value calculated from the observed and expected numbers of individuals with certain genotypes in a population. The chi-square test is a statistical method used to compare observed data with data we would expect to obtain according to a specific hypothesis, in this case, the Hardy-Weinberg equilibrium which states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences.

For the Hardy-Weinberg chi-square calculations, you will use the formula X² = ∑ (O - E)² / E, where O is the observed number and E is the expected number. Plugging in the given values for the three genotypes (hh, hh, hh) provides:

X² = ((87-75)² / 75) + ((145-150)² / 150) + ((68-75)² / 75) = (144 / 75) + (25 / 150) + (49 / 75) = 1.92 + 0.17 + 0.65 = 2.74.

Therefore, the correct chi-square value based on these observations is 2.74, which corresponds to option (a).