Answer:
a. Chi-Square Value = 0.12
b. Degrees of freedom = 1
c. Reject or fail to reject the hypothesis = fail to reject the hypothesis
Step-by-step explanation:
Available data:
- Cross: long wings to flies with mutant, dumpy wings
- F1) 100% long-winged flies
- F2) 672 long-winged flies 218 dumpy-winged flies
- Hypothesis: the dumpy wing is inherited as a recessive trait
Let us name the allele for Long L and the allele for dumpy l
The number of observed individuals:
- Total number: 890 flies (672 + 218)
- Long-winged = 672
- Dump-winged = 218
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
- Chi square= ∑ ((O-E)²/E) = 0.03 + 0.09 = 0.12
- Freedom Degrees = genotypes - alleles = 3 - 2 = 1
- Significance level = 0.05
- Table value/Critical value = 3.84
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.