Question

In: Statistics and Probability

Use the following information to answer questions 43a-43e. You are studying cannibals in Borneo and want...

Use the following information to answer questions 43a-43e.

You are studying cannibals in Borneo and want to determine if a specific village population is in Hardy-Weinberg equilibrium with respect to the single-gene locus segregating the two co-dominant M and N blood type alleles (LM,LN). The following are sample data from this population of the cannibals:

Genotype # individuals
MM 325
MN 680
NN 140
total 1145

a. What is the observed frequency of each genotype?

b. What is the observed frequency of each allele?

c. Based on b, what would the expected frequency of each genotype be, if the population were under Hardy-Weinberg equilibrium?

d. What is the expected number of individuals of each genotype under H-W equilibrium?

e. Perform a Chi-squared analyses to determine whether the observed genotype numbers are consistent with H-W equilibrium. (To determine the degrees of freedom, use the formula DF = # of genotypes - # of alleles).

Solutions

Expert Solution

a.

The observed frequency of each genotype are,

Genotype Observed Frequency
MM 325/1145 = 0.2838428
MN 680/1145 = 0.5938865
NN 140/1145 = 0.1222707

b.

The observed frequency of each genotype are,

Allele Observed Count
M 325 + 680/2 = 665
N 140 + 680/2 = 480

Probability of Allele M, p = 665 / 1145 = 0.580786

Probability of Allele N, q = 480 / 1145 = 0.419214

c.

Expected frequency of each genotype be, if the population were under Hardy-Weinberg equilibrium

Genotype Expected Frequency
MM
MN
NN

d.

Expected number of individuals of each genotype be, if the population were under Hardy-Weinberg equilibrium

Genotype Expected Frequency
MM
MN
NN

e.

Chi-square test statistic

= 55.22245

DF = # of genotypes - # of alleles = 3 - 2 = 1

Critical value of Chi-square test statistic for df = 1 and 0.05 significance level is 3.84

Since Chi Square test statistic is greater than the critical value, we conclude that there is significant evidence that the  observed genotype numbers are not consistent with H-W equilibrium.

orchestra answered 2 years ago
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