In a variety of cattle, horn growth is controlled by alleles at one locus; allel

Question

In a variety of cattle, horn growth is controlled by alleles at one locus; allele H for horned and allele h for hornless. Tail growth is determined by another gene locus; allele T for tail (tail present) and allele t for ‘tailless’ (tail). The upper case alleles are completely dominant. The 2 loci segregate independently. There are no interactions between the loci. A bull with horns and tail, mates with females, all hornless and without tails. They have 100 progenies: 8 hornless and tailless, 60 horned with tail, 21 horned and tailless, and 11 hornless with tail.

a) Assume that the Chi-Square value was calculated to be 69.04. What is the approximate probability (P-value) of observing such phenotypic data?

b) Given the Chi-square value and degrees of freedom, do you “reject” or “fail to reject” the hypothesis that the observed phenotypic data do not deviate from the expected ratio for the phenotypic data? Circle either “reject” or “fail to reject”.

Explanation / Answer

(a)

approximate probability (P-value) is less than 0.005

Look up the chi-square table to find p-value for the corresponding degrees of freedom                  
p-value   <0.05   significant          
                  
Null hypothesis states no difference between observed and expected ratio.                        
If p value is significant then reject null hypothesis          
                  
In this given data                  
There is a significant difference between observed and expected frequencies, therefore the alleles are linked                  
These traits do not assort independently                  

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