i have to do a chi square test based on the genetics of corn. I predicted that the ratio for the results below would be 8:2:2:1 and it works for the chi-square test. but then i have to say what the genotypes would be for each of the parents to match the ratio but i don't think any genotypes for parents would exist. did i do something wrong, what would be the real phenotypic ratio that I could get genotypes of the parent for?
Data:
yellow smooth kernels: 363
Yellow wrinkled kernels: 93
white smooth: 100
white wrinkled: 58
To determine if you did something wrong, let's start by calculating the expected phenotypic ratio based on the 8:2:2:1 ratio you predicted. The expected phenotypic ratio can be calculated by multiplying the total number of offspring by the predicted ratio and then dividing each category by the sum of all categories.
First, let's calculate the sum of all categories:
Total = 363 (yellow smooth) + 93 (yellow wrinkled) + 100 (white smooth) + 58 (white wrinkled) = 614
Now, let's calculate the expected number for each category:
Yellow smooth = (Total) * (8 / 13) = 614 * (8 / 13) ≈ 377.85
Yellow wrinkled = (Total) * (2 / 13) = 614 * (2 / 13) ≈ 59.85
White smooth = (Total) * (2 / 13) = 614 * (2 / 13) ≈ 59.85
White wrinkled = (Total) * (1 / 13) = 614 * (1 / 13) ≈ 29.92
Notice that the expected numbers are not whole numbers. In genetics, the expected ratios are theoretical and may not always yield whole numbers.
Now, let's assess if your predicted ratio matches the observed results using a chi-square test. The chi-square test helps determine whether the observed data significantly deviates from the expected data. The formula to calculate the chi-square value is:
χ² = Σ [(observed - expected)² / expected]
Now let's plug in the values and calculate the chi-square value:
χ² = [(363 - 377.85)² / 377.85] + [(93 - 59.85)² / 59.85] + [(100 - 59.85)² / 59.85] + [(58 - 29.92)² / 29.92]
≈ (563.722 / 377.85) + (781.462 / 59.85) + (163.366 / 59.85) + (790.489 / 29.92)
≈ 1.491 + 13.048 + 2.729 + 26.408
≈ 43.676
Now, let's determine the degrees of freedom (df). The degrees of freedom in a chi-square test are calculated as the number of categories minus 1:
df = number of categories - 1 = 4 - 1 = 3
Next, we need to consult a chi-square distribution table or use statistical software to find the critical value for a chosen significance level (α) and degrees of freedom (df). If the calculated chi-square value is greater than the critical value, it means the observed results significantly deviate from the expected results.
Finally, based on the significance level and degrees of freedom, you can compare the calculated chi-square value to the critical value and determine if the observed data deviates significantly from the expected data. If it does, you would reject the predicted ratio.
As for determining the genotypes of the parents, it is not possible to determine the exact genotypes for each parent solely based on the phenotypic ratios. The genotypes are a reflection of the genetic makeup of the parents, and without further information or genetic tests, we cannot infer the exact genotypes.