Question

Using the symbols G and g for the alleles for coat colour and D and d for the alleles for eye colour. A cross between the animals in the F₁ generation (DdGg X DdGg) gives 9 : 3: 3 : 1 ratio. In the actual cross between the animals in the generation, the numbers of each phenotype obtained in the offspring were:

grey body, dark eyes - 54

grey body, pale eyes - 4

white body, dark eyes - 4

white body, pale eyes - 18

Use a chi-squaretest to determine whether the difference between these observed results is significant.

Accepted Answer

Chi-square test is a statistical test that is used to determine whether differences between observed and expected results are significant.

$χ^{2} = \sum_{}^{} \frac{{(O - E)}^{2}}{E}$

O - observed value

E = expected value

Expected ratio = 9 : 3 : 3 : 1

The number of offspring expected:

grey body, dark eyes = $\frac{9}{16} \times 80 = 45$

grey body, pale eyes = $\frac{3}{16} \times 80 = 15$

white body, dark eyes = $\frac{3}{16} \times 80 = 15$

white body, pale eyes = $\frac{1}{16} \times 80 = 5$

Grey body, dark eyes Grey body, pale eyes White body, dark eyes White body, pale eyes

Observed number (O) 54 4 4 18

Expected number (E) 45 15 15 5

O-E 9 -11 11 13

(O-E)² 81 121 121 169

(O-E)²/E 1.8 8.07 8.07 33.8

$χ^{2} = \sum_{}^{} \frac{{(O - E)}^{2}}{E}$

= 51.74

The chi-square value represents a probability of 0.05 to 3 degrees of freedom = 7.82

The calculated value = 51.74

The calculated value is much higher, hence, the difference between observed and expected results is significant. It occurs due to the linkage of genes located in the same chromosomes.

Mary Jones, Richard Fosbery, Dennis Taylor and, Jennifer Gregory Solutions for Chapter: Inheritance, Exercise 13: Question

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