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Zorluk: KolayDrawing Valid Inferences

During a five-year study of a protected forest reserve, researchers tracked the population of two owl species, the Barn Owl and the Barred Owl. The total land area of the reserve remained unchanged throughout the study, and no other owl species resided in the forest. In the first year, Barn Owls accounted for 70 percent of all owls in the reserve. By the fifth year, although the total number of owls in the reserve had doubled, the proportion of Barn Owls dropped to 40 percent. Throughout the five years, no owls died or migrated out of the reserve.

Based on the information above, which of the following statements must be true? Select all that apply.

  1. The absolute number of Barn Owls in the reserve was higher in the fifth year than in the first year.Cevap
  2. The population of Barred Owls in the reserve more than doubled over the course of the study.Cevap
  3. C
    Barred Owls had a higher average reproduction rate per nesting pair than Barn Owls during the study period.

Cevap

Both the statement indicating an increase in the absolute number of Barn Owls and the statement indicating that the Barred Owl population more than doubled are correct.
The statement regarding Barn Owls is correct because 40 percent of twice the original population (0.80N) is greater than 70 percent of the original population (0.70N). The statement regarding Barred Owls is also correct because Barred Owls increased from 30 percent of the original population (0.30N) to 60 percent of twice the original population (1.20N), quadrupling in absolute count.

Adım Adım Çözüm

1
Define initial population counts in terms of initial total owl count, N.
In Year 1, Barn Owls = 0.70N and Barred Owls = 0.30N.
The passage states Barn Owls accounted for 70% of the total population, leaving Barred Owls as the remaining 30%.
2
Calculate Year 5 population counts using the doubled total population (2N).
In Year 5, Barn Owls = 40% of 2N = 0.80N; Barred Owls = 60% of 2N = 1.20N.
The overall population doubled to 2N, and Barn Owls represented 40% of this doubled total.
3
Compare Year 1 and Year 5 values for each statement.
Barn Owls increased from 0.70N to 0.80N. Barred Owls increased from 0.30N to 1.20N (a 400% final level relative to starting level).
Mathematical calculation proves both numerical statements are logically required by the passage facts, while claims about per-pair birth rates lack support.

Anahtar Kavram

Drawing Valid Inferences using Mathematical Proportion and Population Constraints
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Drawing Valid Inferences

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