In which of the following situations is it reasonable to use the entire population instead of a sample to collect data?(1 point)
Responses
A scientist wants to determine the average age of the trees in a national forest.
A scientist wants to determine the average age of the trees in a national forest.
A teacher wants to know his students’ favorite holiday in all of his math classes.
A teacher wants to know his students’ favorite holiday in all of his math classes.
A university dean wants to estimate the number of students who work and study at the same time.
A university dean wants to estimate the number of students who work and study at the same time.
A store manager wants to know the percentage of customers who prefer cold coffee over hot coffee.
A store manager wants to know the percentage of customers who prefer cold coffee over hot coffee.
In situation 1, it may be reasonable to use the entire population (all of the trees in the national forest) to collect data. This is because the population size may be small enough to collect data on all of the trees, and it may be important to have precise and accurate information about all of the trees in the forest.
In situations 2, 3, and 4, it is not necessary or practical to use the entire population to collect data. Instead, a sample of students or customers can be used to estimate the information needed, which can be more cost-effective and efficient.
A farmer wants to know if her apples are sweet enough for juice. The farm has 12,000 apple trees. Each one has at least 230 apples. The farmer randomly chose 700 trees and picked one apple from each tree for testing. She then generalized that the trees are sweet enough for juice. Is the farmer’s generalization valid?(1 point)
Responses
No, because she did not include all 12,000 trees in the sample.
No, because she did not include all 12,000 trees in the sample.
No, because 700 trees in the sample is too large.
No, because 700 trees in the sample is too large.
Yes, because all the trees in the sample have at least 230 apples.
Yes, because all the trees in the sample have at least 230 apples.
Yes, because the trees in the sample are chosen randomly. The sample size also appears to be large enough to avoid bias.
Yes, because the trees in the sample are chosen randomly. The sample size also appears to be large enough to avoid bias.
The correct response is: Yes, because the trees in the sample are chosen randomly. The sample size also appears to be large enough to avoid bias.
The farmer's generalization is valid because she used a random sample of trees to test the sweetness of the apples. The sample size of 700 trees is also large enough to avoid bias and provide a reasonable estimate of the sweetness of all the trees on the farm. Additionally, the fact that each tree in the sample has at least 230 apples ensures that the sample is representative of the population.
The situations in which it is reasonable to use the entire population instead of a sample to collect data are:
1. A teacher wants to know his students' favorite holiday in all of his math classes. In this case, since the teacher has access to all the students in his math classes, it is reasonable to collect data from the entire population of students.
2. A university dean wants to estimate the number of students who work and study at the same time. In this situation, the university dean wants to gather data on all the students who work and study simultaneously, and since the dean has access to information about all the students in the university, it is reasonable to use the entire population.
It is important to note that in both cases, the entire population can be reasonably accessed for data collection.