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 degrees of freedom for this scenario? (Type in your answer with a digit.)
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 determine the degrees of freedom for this scenario, we need to consider the number of categories in the data and subtract 1. In this case, we have 4 categories: tall green, tall white, short green, and short white. So the degrees of freedom is 4 - 1 = 3.
To calculate the Chi Square value for this data set, we need to compare the observed data with the expected data based on the given genetic ratios.
First, we need to calculate the expected values for each category. Since tall is dominant to short and green is dominant to white, we would expect the following ratios:
- Tall green: 81/160 x 160 = 81
- Tall white: 39/160 x 160 = 39
- Short green: 27/160 x 160 = 27
- Short white: 13/160 x 160 = 13
Next, we calculate the Chi Square value using the formula:
Chi Square = Σ((Observed - Expected)^2 / Expected)
For each category:
- Tall green: ((81 - 81)^2 / 81) = 0
- Tall white: ((39 - 39)^2 / 39) = 0
- Short green: ((27 - 27)^2 / 27) = 0
- Short white: ((13 - 13)^2 / 13) = 0
Summing up these values: 0 + 0 + 0 + 0 = 0.
Therefore, the Chi Square value for this data set is 0 (rounded to the nearest tenth).