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Inheritance: Question 10

Syllabus 16.2

Multiple choice A2 1 mark

In a species of guinea pig, coat colour is controlled by a single gene, with allele C (black, dominant) and allele c (cream, recessive). A breeder crosses two black guinea pigs that are both heterozygous (Cc), expecting offspring in the ratio 3 black : 1 cream if the C and c alleles behave as simple dominant and recessive alleles.

Out of 320 offspring from this cross, the breeder counts 228 black guinea pigs and 92 cream guinea pigs.

Using the formula chi-squared equals the sum of (observed minus expected) squared, divided by expected, which of the following is the calculated value of chi-squared for these results, to 1 decimal place?

Choose an answer to check it, then compare with the worked solution below.
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Worked solution

Step 1: Calculate the expected numbers

If the alleles behave as simple dominant and recessive alleles, the cross Cc x Cc is expected to give offspring in the ratio 3 black : 1 cream. For a total of 320 offspring:

Expected black=34×320=240\text{Expected black} = \frac{3}{4} \times 320 = 240 Expected cream=14×320=80\text{Expected cream} = \frac{1}{4} \times 320 = 80

Step 2: Calculate chi-squared

PhenotypeObserved (O)Expected (E)O - E(O - E)^2(O - E)^2 / E
Black228240-12144144/240 = 0.6
Cream928012144144/80 = 1.8

Summing the final column:

χ2=0.6+1.8=2.4\chi^2 = 0.6 + 1.8 = 2.4

Step 3: Evaluate each option

  • A (0.6): incorrect. This is only the contribution from the black category, not the full sum.
  • B (1.8): incorrect. This is only the contribution from the cream category, not the full sum.
  • C (2.4): correct. This is the sum of both category contributions, 0.6 + 1.8.
  • D (4.8): incorrect. This is double the correct value, as if each contribution had been counted twice.

Final answer

  • χ2=2.4\chi^2 = 2.4, option C.