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1) Mendel formulated the law of independent assortment as his second law of inhe

ID: 3219609 • Letter: 1

Question

1) Mendel formulated the law of independent assortment as his second law of inheritance. It involves two genes independently segregated during reproduction, each independently determining one aspect of the phenotype. In one experiment, Mendel crossed pea plants producing yellow, round seeds with pea plants producing green, wrinkled seeds. The first generation resulted in only plants producing yellow, round seeds. Self- crossing of the F1 yielded the following phenotype F2: Phenotype Yellow Round Yellow Wrinkled Green Round Green wrinkled Counts 315 101 108 32 Assuming two independent genes, each with dominant allele and a recessive allele, we would like to find a 9:3:3:1 phenotype ratio.

a) What are the null and alternative hypotheses for chi-square goodness-of-fit test?

b) What are the expected counts under the null hypothesis?

c) Calculate the value of the chi-square test statistic d) Do the data agree with Mendel’s second law of genetic inheritance? e) Compare your results by chisq.test in R to perform the test?

Explanation / Answer

a) Null Hypothesis: the given data follow the given ratios 9:3:3:1

Alternative hypothesis: the given data not follow the given ratios 9:3:3:1

b) The expected frequenceis are calculated as follows

Ei = (ratio) * 556 / 16 i = 1,2,3,4

c)

The chisquare contribution is

Num Categories: 4
Degrees of freedom: 3

Test Statistic, X^2: 0.4700
Critical X^2: 7.814736
P-Value: 0.9254

Here P-value > alpha 0.05, we accept H0

Thus, we conclude that  the given data follow the given ratios 9:3:3:1

d) Yes the data agree with Mendel’s second law of genetic inheritance

e) R-Script:

counts=c(315,101,108,32)
expected=c(312.75,104.25,104.25,34.75)
chisq.test(counts, expected)

(Oi) Expected Counts Ratio Counts (Ei) 315 9 312.75 101 3 104.25 108 3 104.25 32 1 34.75 Total: 556 16 556