Two samples of fish from a pond were analyzed. The second sample was taken six months after the first sample.
| | Sample 1 | Sample 2 |
| :----- | :------- | :------- |
| Trout | 3 | 5 |
| Catfish| 9 | 9 |
| Bass | 8 | 6 |
| All Fish | 20 | 20 |
Which are valid inferences? Check all that apply.
A. The second sample shows the same amount of each type of fish in the pond.
B. About twice as many trout were in the pond at the time the second sample was taken.
C. About the same number of bass were found in the two samples.
D. Fewer bass were in the pond at the time the second sample was taken.
E. About the same number of catfish were found in both samples.
Answer (2)
The second sample does not show the same amount of each type of fish.
The number of trout in the second sample is not about twice the number in the first sample.
The number of bass is approximately the same in both samples.
There were fewer bass in the second sample.
The number of catfish is about the same in both samples.
Valid inferences:
About the same number of bass were found in the two samples.
Fewer bass were in the pond at the time the second sample was taken.
About the same number of catfish were found in both samples.
Explanation
Analyze the problem and data We are given two samples of fish from a pond, taken six months apart. We need to determine which of the given inferences are valid based on the data provided in the table.
Evaluate each inference Let's analyze each inference:
The second sample shows the same amount of each type of fish in the pond.
This is incorrect. The number of trout and bass changed between the samples.
About twice as many trout were in the pond at the time the second sample was taken.
Sample 1 has 3 trout, and sample 2 has 5 trout. Since 3 e q 5/2 , this statement is not accurate. However, 2 e q 5/3 . Thus, the number of trout in the second sample is not about twice the number in the first sample. So, this statement is not valid.
About the same number of bass were found in the two samples.
Sample 1 has 8 bass, and sample 2 has 6 bass. These numbers are relatively close, so this statement could be considered valid.
Fewer bass were in the pond at the time the second sample was taken.
Sample 1 has 8 bass, and sample 2 has 6 bass. Since 6 is less than 8, this statement is valid.
About the same number of catfish were found in both samples.
Both samples have 9 catfish. This statement is valid.
Identify valid inferences Based on our analysis, the valid inferences are:
About the same number of bass were found in the two samples.
Fewer bass were in the pond at the time the second sample was taken.
About the same number of catfish were found in both samples.
Examples
Understanding population changes in ecosystems is crucial for conservation efforts. For example, tracking fish populations in a pond can help assess the impact of environmental changes or management strategies. By analyzing samples taken at different times, we can infer trends and make informed decisions about how to protect these populations. This type of analysis is also used in wildlife management, agriculture, and public health to monitor and respond to changes in populations.
The valid inferences from the fish samples are that fewer bass were present in the second sample and that the same number of catfish were found in both samples. The other options regarding trout and bass comparisons are not accurate. The data suggests changes in fish populations over time, which are essential for ecological studies.
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