Question

Practice Problems:

1. Test the following data to see if it conforms to the 9:3:3:1 ratio predicted from a dihybrid cross of corn plants heterozygous for round, yellow seeds:

315 round yellow

108 round green

101 wrinkled yellow

32 wrinkled green

A total of 556 seeds were counted!

2. Test the following data to see if it conforms to the 9:3:3:1 ratio predicted from a dihybrid cross of corn plants heterozygous for the purple—starchy traits:

271 Purple—starchy

73 purple—sweet

63 yellow—starchy

26 yellow—sweet

A total of 433 seeds were counted!

Answer 1

1. To solve a genetic experiment to check if the data fits 9:3:3:1 ratio under Mendelian genetics, we can prrform a statistical test that can test out ratios is the Chi-Square or Goodness of Fit test.

The formula is as follows:-

Chi-Square Formula

Degrees of freedom (df) = n-1 where n is the number of classes

We need to test the following data given in question to determine if it fits a 9:3:3:1 ratio.

Observed Values	Expected Values
315 Round, Yellow Seed	(9/16)(556) = 312.75 Round, Yellow Seed
108 Round, Green Seed	(3/16)(556) = 104.25 Round, Green Seed
101 Wrinkled, Yellow Seed	(3/16)(556) = 104.25 Wrinkled, Yellow
32 Wrinkled, Green	(1/16)(556) = 34.75 Wrinkled, Green
556 Total Seeds	556.00 Total Seeds

= {(315-312.75)2 / 312.75} + {(108-1.04.25)2 / 104.25} + {(101-104.25)2 / 104.25} + {(32-34.75)2/34.75}

= 0.47

Number of classes (n) = 4 df = n-1 = 4-1 = 3

Calculated Chi-square value = 0.47

Table Chi-square value = 7.82 at 0.05 probablity

If we see the Chi-Square table at df = 3, then it can be aeen that the probability of chi-square value is greater than 0.90. By statistical convention, use the 0.05 probability level as critical value. When the calculated chi-square value is found to be less than the 0 .05 value given in chart for 3 degree of freedom, we accept the null hypothesis.As because the calculated chi-square value 0.47 is lesser than the chart value of 7.82 at 0.05 probability; we accept the hypothesis that the data fits a 9:3:3:1 ratio.

Similarly for problem no 2… we would again perform a chi square test.

Please check the attached image for the calculations of problem no. 2.