Refer to this passage for the remaining questions: In corn plants, tall is dominant to short and green is dominant to albino. A corn plant that is heterozygous for both height and color mates with itself and produces 160 seeds. After planting, those seeds germinate and show the following phenotypic distribution: 81 tall green ones, 39 tall white ones, 27 short green ones, and 13 short white ones. The corn breeder sees the discrepancies between expected data and these observed data and wonders whether a mutation must have happened to explain the discrepancies.
What is the Chi Square value for this data set? Round to the nearest tenth. (If you want this question to give you good predictive feedback about future test performance, you should be calculating Chi Square the old way, meaning without the spreadsheet).
To calculate the Chi Square value for this data set, we need to compare the observed phenotypic distribution with the expected distribution based on the given ratios.
Let's start by determining the expected distribution. Since tall is dominant to short and green is dominant to white, we can calculate the expected proportions by multiplying the individual probabilities.
The original parent individual was heterozygous for both height and color, so the genotype would be TtGg.
To determine the expected distribution, we need to perform a cross between TtGg and TtGg:
Possible genotypes:
- TTGG (tall and green)
- TTGg (tall and green)
- TtGG (tall and green)
- TtGg (tall and green)
- TTgg (tall and white)
- Ttgg (tall and white)
- ttGG (short and green)
- ttGg (short and green)
- ttgg (short and white)
Based on Mendelian genetics, we can expect a phenotypic ratio of 9:3:3:1 for tall green, tall white, short green, and short white phenotypes respectively.
Out of the total 160 seeds, we can calculate the expected number of each phenotype as follows:
Expected tall green: 160 * (9/16) = 90
Expected tall white: 160 * (3/16) = 30
Expected short green: 160 * (3/16) = 30
Expected short white: 160 * (1/16) = 10
Now that we have the expected and observed values, we can calculate the Chi Square value using the formula:
χ² = Σ((O - E)² / E)
where:
χ² is the Chi Square value
Σ signifies that we sum up the values
O is the observed value
E is the expected value
Calculating for each phenotype:
For tall green:
(81 - 90)² / 90 = 0.9
For tall white:
(39 - 30)² / 30 = 3
For short green:
(27 - 30)² / 30 = 0.3
For short white:
(13 - 10)² / 10 = 0.9
Now we sum up the individual Chi Square values:
χ² = 0.9 + 3 + 0.3 + 0.9 = 5.1
Therefore, the Chi Square value for this data set is 5.1 (rounded to the nearest tenth).