According to a genetics model, plants of a particular species occur in the categories A, B, C, and D, in the ratio 9:3:3:1. The categories of different plants are mutually independent. At a lab that grows these plants, 218 are in Category A, 69 in Category B, 84 in Category C, and 29 in Category D.
Under the null, the expected number of plants in Category D is ______.
Degrees of freedom = _______.
Under the null, the expected number of plants in Category D is 25.
Calculation: 1/16 = x/400; x = 25
Note: 400 is the total number of plants in all categories.
Degrees of freedom = 3 (df = number of groups minus 1).
To determine the expected number of plants in Category D under the null, we need to use the given ratio of 9:3:3:1.
First, let's calculate the total number of plants:
Total Number of Plants = Number of Category A Plants + Number of Category B Plants + Number of Category C Plants + Number of Category D Plants
Total Number of Plants = 218 + 69 + 84 + 29 = 400
Next, let's calculate the expected number of plants in Category D:
Expected Number of Plants in Category D = Total Number of Plants * (Ratio of Category D)
Expected Number of Plants in Category D = 400 * (1/16) = 25
Therefore, the expected number of plants in Category D under the null is 25.
Now, let's determine the degrees of freedom. The degrees of freedom (df) represent the number of categories that can vary freely in a statistical analysis. In this case, we have four categories (A, B, C, and D), but since the categories are mutually independent and are specified by the genetic model, only three categories can vary freely.
Therefore, the degrees of freedom (df) in this scenario would be 3.