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.
1. The null hypothesis is:
a)The model is good.
b)The model isn't good.
c)Too many of the plants are in Category C.
d)The proportion of plants in Category A is expected to be 9/16; the difference in the sample is due to chance.
2.The alternative hypothesis is:
a)The model is good.
b)The model isn't good.
c)Too many of the plants are in Category C.
d)The proportion of plants in Category A is expected to be 9/16; the difference in the sample is due to chance.
3. Under the null, the expected number of plants in Category D is ______.
4. Degrees of freedom = _______.
1. The null hypothesis is: d) The proportion of plants in Category A is expected to be 9/16; the difference in the sample is due to chance.
To arrive at this answer, we need to understand that the null hypothesis refers to the assumption we want to test or prove wrong. In this case, the null hypothesis states that the proportion of plants in Category A is expected to be 9/16 (as predicted by the genetics model), and any difference in the sample is purely due to chance. Therefore, option d) is the correct answer.
2. The alternative hypothesis is: b) The model isn't good.
The alternative hypothesis represents the opposite of the null hypothesis, expressing the claim or theory that counters the null hypothesis. In this case, option b) is the correct answer as it states that the model isn't good, indicating a disagreement with the predicted proportions.
3. Under the null, the expected number of plants in Category D is calculated as follows:
Total number of plants = 218 + 69 + 84 + 29 = 400
Since the ratio of plants in categories A, B, C, and D is given as 9:3:3:1, we can calculate the expected number of plants in Category D proportional to the total number of plants:
Expected number of plants in Category D = (1/16) * Total number of plants
= (1/16) * 400
= 25
Therefore, the expected number of plants in Category D under the null hypothesis is 25.
4. Degrees of freedom = number of categories - 1
In this case, the number of categories is 4 (A, B, C, D), so the degrees of freedom would be 4-1=3.