In the laboratory, a genetics student crossed flies with normal, long wings to flies with mutant, dumpy wings, which she believed was a recessive trait. In the F1, all flies had long wings. In the F2, the following results were obtained: 672 long-winged flies 218 dumpy-winged flies The student tested the hypothesis that the dumpy wing is inherited as a recessive trait by performing chi-square analysis of the F2 data. Determine:
a. Chi-Square Value.
b. Degrees of freedom.
c. Reject or fail to reject the hypothesis.

a. Chi-Square Value = 0.12

b. Degrees of freedom = 1

c. Reject or fail to reject the hypothesis = fail to reject the hypothesis

Explanation:

Available data:

Let us name the allele for Long L and the allele for dumpy l

The number of observed individuals:

In the F2 generation, if l was a recessive allele and L a dominant allele, exhibiting complete dominance, we would expect a 3:1 phenotypic ratio.

Cross:          Ll   x   Ll

Gametes)   L   l    L  l

Punnett square)   L     l

                     L    LL    Ll

                      l     lL     ll

F2) 3/4 LL + Ll long-winged individuals

      1/4 ll dump-winged individuals

From this ratio and the total number of individuals in the F2 generation, we can get the expected number of individuals:

4 possible genotypes 890 individuals

3 LL + Ll genotype X = 667.5 long-winged individuals

1 ll genotype X = 222.5 dump-winged individuals

Chi square = ∑ (O-E)²/E

LL + Ll = (O-E)² /E

LL+ Ll = (672 - 667.5) ² / 667.5

LL + Ll = 0.03

ll= (O-E)²/E        

ll= (218 - 222.5)² / 222.5

ll= 0.09  

0.12 < 3.84 meaning that there is enough evidence to reject the null hypothesis.

Fail to reject the hypothesis.  The genotypes in the population might be in equilibrium H-W. L is the dominant allele, and l is the recessive allele. The dumpy wing is inherited as a recessive trait.

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sorry, but you do not have posted the diagram.