Question

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

Explanation:

Step1: Calculate total number of offspring

$729 + 721+28 + 22=1500$

Step2: Determine observed recombinant and non - recombinant numbers

Observed recombinants: $28 + 22=50$. Observed non - recombinants: $729+721 = 1450$

Step3: Calculate expected recombinant and non - recombinant numbers

Expected recombinant number: $0.04\times1500 = 60$. Expected non - recombinant number: $(1 - 0.04)\times1500=0.96\times1500 = 1440$

Step4: Calculate chi - square value for recombinants

$\frac{(50 - 60)^2}{60}=\frac{(- 10)^2}{60}=\frac{100}{60}\approx1.67$

Step5: Calculate chi - square value for non - recombinants

$\frac{(1450 - 1440)^2}{1440}=\frac{10^2}{1440}=\frac{100}{1440}\approx0.07$

Step6: Calculate total chi - square value

$\chi^{2}=1.67+0.07 = 1.74$

Answer:

$1.74$