QUESTION 11 1. Through PCR, we have determined the PER3 genotypes for a class of students as follows: H4/H4 = 125 individuals; H4/H5 = 85 individuals and H5/H5=24 individuals. Using the allele's frequencies experimentally derived, calculate the frequency of the H4/H5 genotype that would be expected if the class were a population in Hardy-Weinberg equilibrium. 1. 0.28 2. 0.51 3. 0.19 4. 0.72 5. 0.14 6. 0.24 7. 0.41 QUESTION 12 1. Through PCR, we have determined the PER3 genotypes for a class of students as follows: H4/H4 = 125 individuals; H4/H5 = 85 individuals and H5/H5=24 individuals. Using the genotype frequencies derived assuming that the class were a population in Hardy-Weinberg equilibrium, calculate the number of H4/H4 individuals that would be expected in the class (rounded numbers). 1. 19 2. 57 3. 72 4. 147 5. 171 6. 120 7. 96 QUESTION 13 1. Through PCR, we have determined the PER3 genotypes for a class of students as follows: H4/H4 = 125 individuals; H4/H5 = 85 individuals and H5/H5=24 individuals. Considering the Hardy Weinberg equilibrium and comparing the observed and the expected number of individuals for the three genotypes, calculate the value of the Chi-square statistic 1. 2.69 2. 0.05 3. 28.67 4. 14.59 5. 0.50 6. 22.31 7. 3.84 QUESTION 14 1. Through PCR, we have determined the PER3 genotypes for a class of students as follows: H4/H4 = 125 individuals; H4/H5 = 85 individuals and H5/H5=24 individuals. Considering the Hardy Weinberg equilibrium, which is the (correct) null hypothesis tested by Chi-square? 1. The whole class represents a population that is in Hardy-Weinberg equilibrium 2. The whole class represents a population that may not be in Hardy-Weinberg equilibrium 3. The whole class represents a population that is not in Hardy-Weinberg equilibrium 4. The whole class represents a population that may be in Hardy-Weinberg equilibrium QUESTION 15 1. Through PCR, we have determined the PER3 genotypes for a class of students as follows: H4/H4 = 125 individuals; H4/H5 = 85 individuals and H5/H5=24 individuals. Considering the Hardy Weinberg equilibrium and calculating the Chi-square statistic, do you reject or fail to reject the null-hypothesis? 1. Comparing the value of Chi-square that I calculated with the critical value of Chi-square for the appropriate degrees of freedom I conclude that P>0.05. Hence, I reject the null hypothesis. 2. Comparing the value of Chi-square that I calculated with the critical value of Chi-square for the appropriate degrees of freedom, I conclude that P>0.05. Hence, I fail to reject the null hypothesis. 3. Comparing the value of Chi-square that I calculated with the critical value of Chi-square for the appropriate degrees of freedom I conclude that P<0.05. Hence, I reject the null hypothesis. 4. Comparing the value of Chi-square that I calculated with the critical value of Chi-square for the appropriate degrees of freedom I conclude that P<0.05. Hence, I fail to reject the null hypothesis.

According to Hardy-Weinberg, when a population is in equilibrium, it will have the same allelic frequencies generation after generation, meaning that they are stable, they are not evolving.

When any evolutive force is acting on the population, this equilibrium breacks, and allelic and genotypic frequencies change through generations, differing from the expected ones.  

A) Option 7 is the correct answer ⇒ 0.41

B) Option 6 is the correct answer ⇒ 120

C) Option 7 is the correct answer ⇒ 3.84

D) Option 1 is the correct answer ⇒ The class represents a population that is in H-W equilibrium

E) Option 1 is correct. Comparing the value of Chi-square that I calculated with the critical value of Chi-square for  the appropriate degrees of freedom I conclude that P>0.05. Hence, I reject the null hypothesis.

Allelic frequencies in a locus are represented as p and q, referring to the

allelic dominant or recessive forms. The genotypic frequencies after one generation are p² (H0m0zyg0us  dominant), 2pq (H3ter0zygous), q² (H0m0zyg0us recessive). Populations in H-W equilibrium will get the same

allelic frequencies generation after generation.

The sum of the allelic frequencies equals 1, this is p + q = 1.

In the same way, the sum of genotypic frequencies equals 1, this is

p² + 2pq + q² = 1

Being

 p the dominant allelic frequency,

 q the recessive allelic frequency,

 p² the h0m0zyg0us dominant genotypic frequency

 q² the h0m0zyg0us recessive genotypic frequency

 2pq the h3ter0zyg0us genotypic frequency

Situation: Through PCR, we have determined the PER3 genotypes for a class of students as follows:

 H4/H4 = 125 individuals;

 H4/H5 = 85 individuals;

 H5/H5=24 individuals.

⇒ Total number of individuals= 125 + 85 + 24 = 234

⇒ Genotypic frequencies, F(xx):

 F(H4/H4) = 125/234 =0.534

 F(H4/H5) = 85/234 = 0.363

 F(H5/H5) = 24/234 = 0.102

⇒ Allelic frequencies, f(x):

 f(H4) = p = F(H4/H4) + 1/2 F(H4/H5) = 0.534 + 0.363/2 = 0.534 + 0.182 = 0.716

 f(H5) = q = F(H5/H5) + 1/2 F(H4/H5) = 0.102 + 0.363/2 = 0.102 + 0.182 = 0.284

Questions:

A)  According to the theoreticall frame, we know that 2pq is the h3ter0zygous genotypic frequency. So,  

F(H4/H5) = 2pq = 2 x 0.716 x 0.284 = 0.408 ≅ 0.41 ⇒ Option 7 is the correct answer.

B)  According to the theoreticall frame, we know that p² is the h0m0zyg0us genotypic frequency. So,

p = 0.716

p² = 0.5126 ≅ 0.513 ⇒ This is the genotypic frequency.

To calculate the number of individuals carrying this genotype, we need to multiply it by the total number of

individuals.

H4/H4 individuals = p² x total number of individuals = 0.513 x 234 = 120

Option 6 is the correct answer.

C)  Up to here we know that 2pq = 0.41 and p² = 0.513

Now we need to calculate q ²

q = 0.284, then q² = 0.284² = 0.08

These are the expected frequencies if the population was in H-W equilibrium.

The expected number of individuals with each genotype are:

 H4/H4 = 0.513 x 234 = 120 individuals

 H4/H5 = 0.41 x 234 = 96 individuals

 H5/H5= 0.08 x 234 = 18 individuals

The observed number of individuals with each genotype are:

 H4/H4 = 125 individuals

 H4/H5 = 85 individuals

 H5/H5=24 individuals

X² = ∑ (Observed - Expected)²/Expected)

X² = ((125-120)²/120) + ((85 - 96)²/96) + ((24-18)²/18)

X² = 0.21 + 1.26 + 2 =

X² = 3.47

The clossest option is option 7 = 3.84. The difference might be related to decimals and rounding.

D)  The correct answer is  1 ⇒ The whole class represents a population that is in Hardy-Weinberg equilibrium

The null hypothesis always predict that populations are in H-W equilibrium.

E)  

 X² = 3.47

 Freedom degrees = n - 1 = 3 - 1 = 2

 Table p value: 7.82

 Significance level, 5% = 0.05

 Table value/Critical value = 5.991

5.991 > 0.347

Meaning that the difference between the observed individuals and the expected individuals is statistically  significant. Not probably to have differe by random chances. There is enough evidence to reject the null

hypothesis.

Option 1 is correct. Comparing the value of Chi-square that I calculated with the critical value of Chi-square for  the appropriate degrees of freedom I conclude that P>0.05. Hence, I reject the null hypothesis.

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