21.24 Gregor Mendel has been called the “father of genetics,” having formulated

Question

21.24 Gregor Mendel has been called the “father of genetics,” having formulated laws of inheritance even before the function of DNA was discovered. In one famous experiment with peas, he crossed pure breeds of tall and dwarf pea plants. The first-generation pea plants were all tall. In the second generation (F2), he obtained 787 tall plants and 277 dwarf plants. Mendel’s first law of inheritance is a model with a dominant and a recessive phenotype. The first law says that we can expect a 3:1 ratio, that is, 3/4 with the dominant and 1/4 with the recessive phenotype, in F2.

(a)Are the conditions for a chi-square goodness-of-fit test satisfied?

(b)What are the null and alternative hypotheses for this test?

(c)What are the expected counts under the null hypothesis?

(d)Compute the chi-square statistic and use software or Table D to find the P-value.What can you conclude? Do these data support Mendel’s first law?

Explanation / Answer

a) Assumptions:

Counted data condition: Counts of number of plant sin each category is available.

Independence assumption: The number of dominant and recessive phenotype are independent of each other.

Randomization condition: It is an experiment, therefore, randomization condition is met.

Expected cell frequency: Expected frequency for dominant phenotype is 1064*3/4=798 and expected frequency of recessive phenotype is 1064*1/4=266 are all satifies the atleast 5 condition.

All assumptions are met, use 2-1=1 degrees of freedom to calculate Chi-sqaure test statistic.

b) H0: The traits occur in predicted proportion.

H1: The trait sdo not occur in predicted proportion.

c) Expected counts:

Tall plants: 1064*0.75=798

Dwarf plants: 1064*0.25=266

d) X^2=Summation (Observed-Expected)^2/Expected

=(787-798)^2/798+(266-277)^2/277

=0.606516

The p value is 0.436. The p value is not less than alpha=0.05. Therefore, fail to reject null hypothesis. There is not sufficient sample evidence to concude that the traits do not occur in predicted proportion.

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