A genetics class decides to re-create the garden pea breeding experiments of Gre

Question

A genetics class decides to re-create the garden pea breeding experiments of Gregor Mendel. They grow several garden pea plants from random crosses of purple-flowered plants and test whether the resulting purple flower:white flower ratio is consistent with the expected 3:1 ratio, based on independent assortment of alleles. A concern is that the initial parental plants might have had a low level of heterozygosity, meaning the frequency of purple-flowered offspring could be higher than expected.

If a sample of plants that contained 80% purple flowered plants produced a Chi-squared value of 4 for a Goodness of Fit test, what was the sample size?

Explanation / Answer

Let n = sample size

Hence, the expected values are, as they are of ratio 3:1,

E(purple) = 0.75n
E(white) = 0.25n

Also, the observed values are

O(purple) = 0.80n
O(white) = 0.20n

Hence, as chi^2 = Sum[(E-O)^2/E], then

(0.75n-0.80n)^2/(0.75n) + (0.25n - 0.20n)^2/(0.25n) = 4

0.003333333n + 0.01n = 4

0.013333333n = 4

n = 300 [ANSWER]

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