post activity questions:
1. imagine a population of 800 individuals, of which 14% have a recessive genetic condition.
a. what is the frequency of homozygous recessive individuals? (think q²)
b. how many individuals have the condition?
c. what is the frequency of the allele causing the recessive condition? (think q)
d. what is the frequency of homozygous dominant individuals? (think p²)
e. how many individuals are heterozygous?
2. if the frequency of a recessive allele is 0.3, what is the frequency of the dominant allele?
3. if the frequency of the homozygous dominant genotype is 0.49, what is the frequency of the dominant allele?
4. if the frequency of the homozygous dominant genotype is 0.49, what is the frequency of the homozygous recessive genotype?
5. which hardy-weinberg equation relates the frequencies of the alleles at a particular gene locus?
6. which hardy-weinberg equation relates the frequencies of the genotypes for a particular gene locus?
7. how would you determine if the change in allele frequencies between two generations is statistically different? what statistical test would you need to run?

Question

post activity questions:
1. imagine a population of 800 individuals, of which 14% have a recessive genetic condition.
   a. what is the frequency of homozygous recessive individuals? (think q²)
   b. how many individuals have the condition?
   c. what is the frequency of the allele causing the recessive condition? (think q)
   d. what is the frequency of homozygous dominant individuals? (think p²)
   e. how many individuals are heterozygous?
2. if the frequency of a recessive allele is 0.3, what is the frequency of the dominant allele?
3. if the frequency of the homozygous dominant genotype is 0.49, what is the frequency of the dominant allele?
4. if the frequency of the homozygous dominant genotype is 0.49, what is the frequency of the homozygous recessive genotype?
5. which hardy-weinberg equation relates the frequencies of the alleles at a particular gene locus?
6. which hardy-weinberg equation relates the frequencies of the genotypes for a particular gene locus?
7. how would you determine if the change in allele frequencies between two generations is statistically different? what statistical test would you need to run?

Accepted Answer

### Question 1a
# Explanation:
## Step1: Identify $ q^2 $
The problem states 14% have the recessive condition. $ q^2 $ is the frequency of homozygous recessive, so convert 14% to decimal.
$ q^2 = \frac{14}{100} = 0.14 $
# Answer:
0.14

### Question 1b
# Explanation:
## Step1: Calculate number with condition
Total population is 800, and 14% have the condition. Multiply total by 0.14.
$ 800 \times 0.14 = 112 $
# Answer:
112

### Question 1c
# Explanation:
## Step1: Find $ q $ from $ q^2 $
Take square root of $ q^2 = 0.14 $.
$ q = \sqrt{0.14} \approx 0.374 $ (rounded to three decimal places)
# Answer:
Approximately 0.374

### Question 1d
# Explanation:
## Step1: Find $ p $ using $ p + q = 1 $
We know $ q \approx 0.374 $, so $ p = 1 - q = 1 - 0.374 = 0.626 $
## Step2: Calculate $ p^2 $
$ p^2 = (0.626)^2 \approx 0.392 $ (rounded to three decimal places)
# Answer:
Approximately 0.392

### Question 1e
# Explanation:
## Step1: Find frequency of heterozygotes ($ 2pq $)
We have $ p \approx 0.626 $, $ q \approx 0.374 $, so $ 2pq = 2 \times 0.626 \times 0.374 \approx 0.464 $
## Step2: Calculate number of heterozygotes
Multiply frequency by total population (800): $ 800 \times 0.464 = 371.2 \approx 371 $ (or keep as 371.2 if decimal is okay)
# Answer:
Approximately 371 (or 371.2)

### Question 2
# Explanation:
## Step1: Use $ p + q = 1 $
Given $ q = 0.3 $, so $ p = 1 - q = 1 - 0.3 = 0.7 $
# Answer:
0.7

### Question 3
# Explanation:
## Step1: Find $ p $ from $ p^2 $
Given $ p^2 = 0.49 $, take square root: $ p = \sqrt{0.49} = 0.7 $
# Answer:
0.7

### Question 4
# Explanation:
## Step1: Find $ p $ from $ p^2 = 0.49 $
$ p = \sqrt{0.49} = 0.7 $
## Step2: Find $ q $ using $ p + q = 1 $
$ q = 1 - p = 1 - 0.7 = 0.3 $
## Step3: Calculate $ q^2 $
$ q^2 = (0.3)^2 = 0.09 $
# Answer:
0.09

### Question 5
# Brief Explanations:
The Hardy - Weinberg equation that relates allele frequencies at a gene locus is $ p + q = 1 $, where $ p $ is the frequency of the dominant allele and $ q $ is the frequency of the recessive allele. This equation is based on the fact that the sum of the frequencies of all alleles at a locus in a population must equal 1 (since they are the only alleles present for that gene in the population).
# Answer:
$ p + q = 1 $

### Question 6
# Brief Explanations:
The Hardy - Weinberg equation that relates genotype frequencies for a gene locus is $ p^{2}+2pq + q^{2}=1 $. Here, $ p^{2} $ is the frequency of homozygous dominant individuals, $ 2pq $ is the frequency of heterozygous individuals, and $ q^{2} $ is the frequency of homozygous recessive individuals. The sum of the frequencies of all genotypes in a population must equal 1.
# Answer:
$ p^{2}+2pq + q^{2}=1 $

### Question 7
# Brief Explanations:
To determine if the change in allele frequencies between two generations is statistically different, we can use a chi - square ($ \chi^{2} $) test. First, we would calculate the expected allele frequencies in the second generation under the Hardy - Weinberg equilibrium (assuming no evolutionary forces are acting, which is the null hypothesis). Then we would calculate the observed allele frequencies in the second generation. The chi - square test statistic is calculated as $ \chi^{2}=\sum\frac{(O - E)^{2}}{E} $, where $ O $ is the observed frequency and $ E $ is the expected frequency. If the calculated chi - square value is greater than the critical value (from the chi - square distribution table, based on the degrees of freedom), we reject the null hypothesis and conclude that the allele frequencies have changed significantly.
# Answer:
To determine if the change in allele frequencies between two generations is statistically different, we can use a chi - square ($ \chi^{2} $) test. We compare the observed allele frequencies with the expected frequencies (under Hardy - Weinberg equilibrium) using the formula $ \chi^{2}=\sum\frac{(O - E)^{2}}{E} $, where $ O $ is the observed frequency and $ E $ is the expected frequency. If the calculated $ \chi^{2} $ value exceeds the critical value (from the chi - square distribution table), the change is statistically significant.

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QUESTION IMAGE

Question

Explanation:

Question 1a

Step1: Identify \( q^2 \)

Step1: Calculate number with condition

Step1: Find \( q \) from \( q^2 \)

Answer:

Question 1b