Question

question 4 of 9 recall the table from question #3. genotype/phenotype results (number) aabb (purple, long) 729 aabb (red, round) 721 aabb (purple, round) 28 aabb (red, long) 22 prior research has suggested that the actual recombination rate between these loci is 4 percent. in order to determine whether the difference between the observed recombination frequency of 3.3% and the expected recombination frequency of 4% is due to chance sampling error or is indicative of some actual difference, we perform a statistical test. in this case, the chi - square test is appropriate. the chi - square test statistic is calculated with the following formula: $chi_{s}^{2}=sum_{i = 1}^{c}\frac{(o_{i}-e_{i})^{2}}{e_{i}}$ o is the observed value, e is the expected value, and c is the categories - in this case, recombinant and non - recombinant offspring. in this case, if the test statistic is greater than the critical value of 3.841, then the null hypothesis can be rejected. the first step is to determine the observed and expected numbers of recombinant and non - recombinant phenotypes. observed expected recombinant

Explanation:

Step1: Calculate total number of offspring

The total number of offspring is the sum of all observed values: $729 + 721+28 + 22=1500$.

Step2: Determine observed number of recombinants

The recombinant phenotypes are $Aabb$ and $aaBb$. So the observed number of recombinants $O = 28+22 = 50$.

Step3: Determine expected number of recombinants

The expected recombination frequency is $4\%$ or $0.04$. So the expected number of recombinants $E=0.04\times1500 = 60$.

Step4: Determine observed number of non - recombinants

The non - recombinant phenotypes are $AaBb$ and $aabb$. So the observed number of non - recombinants $O_{nr}=729 + 721=1450$.

Step5: Determine expected number of non - recombinants

The expected non - recombination frequency is $1 - 0.04=0.96$. So the expected number of non - recombinants $E_{nr}=0.96\times1500 = 1440$.

Step6: Calculate chi - square statistic

Using the formula $\chi^{2}=\sum_{i = 1}^{C}\frac{(O_{i}-E_{i})^{2}}{E_{i}}$, we have two categories (recombinant and non - recombinant).
For recombinants: $\frac{(50 - 60)^{2}}{60}=\frac{(- 10)^{2}}{60}=\frac{100}{60}\approx1.67$.
For non - recombinants: $\frac{(1450 - 1440)^{2}}{1440}=\frac{10^{2}}{1440}=\frac{100}{1440}\approx0.07$.
$\chi^{2}=1.67+0.07 = 1.74$.

Answer:

The chi - square statistic is approximately $1.74$.