Question

A newly identified frog mutant, persistent tail (retains the tail through metamorphosis), is hypothesized to be autosomal dominant. The experimenter started with homozygous wild type virgin females and homozygous persistent tail males. The data from the F2 generation was 83 wild type males, 111 wild type females, 141 persistent tail males and 211 persistent tail females. Does this data support or reject the hypothesis? Use chi-square to prove your position.

Answer 1

Given that,

Number of persistent (mutant) tail males= 141

Number of persistent (mutant) tail females = 211

Number of wild type males = 83

Number of wild type females = 111

Total mutant type 141+211 = 352

Total wild type 83+111= 194

If the persistent tail (retains the tail through metamorphosis), is an autosomal dominant gtrait, we must get a 3:1 ratio for mutant type : wild type

ie If the ratio of total mutant : Total wild follow 3:1 ratio, we can say that the trait is autosomal dominant

Threfore, our Null Hypithesis is and Alternative Hypothesis is as follows

Null Hypithesis = Ratio of total mutant to Total wild is not significantly different (ie follow 3:1 ratio)

Alternative Hypothesis = rRatio of total mutant to Total wild is significantly different (ie do not follow 3:1 ratio)

. To test this hypothesis we have to carryout a Chisquare (X2) test

Our Null Hypithesis is - Ratio of total mutant to total wild is not significantly different (ie follow 3:1 ratio)

Here at 1 degrees of freedom (2-1=1), and 0.05 probability level the calculated value of χ² (32.29) is greater than tabled value (3.841). Therefore the Null hypothesis is rejected and alternative hypothesis is accepted

ie Ratio of total mutant to Total wild is significantly different and do not follow 3:1 ratio

So, our chisquare test revealed that, the number of mutant to wild do not follow 3:1 ratio. This means that, our hypotheis is wrong and the mutant trait (persistent tail) is not autosomal dominant