A common statistical method for estimating a population size assumes each member of the population has an equal probability of being captured. To assess this assumption for crocodile populations, investigators repeatedly sampled sections of rivers in Australia. Crocodile lengths were measured in size classes. Crocs 0.0 - 0.3 meters in length are in size class 1, 0.3 - 0.6 meters in length are size class 2, etc. The normal maximum adult length is in a class size of 9 or 10. The investigators fit a quadratic function relating the probability of capture and the size class of captured crocodiles. The output from their analysis is shown below. Polynomial Fit Degree=2
PrCap = 0.66 + 0.77Class − 0.01(Class)^2
(a)What proportion of the variability in probability of capture is explained by the crocodile's size class?
(b)Some biologists speculate that as crocodiles grow they become more wary of humans, and are more difficult to detect in the wild. Support or refute this belief by appealing to the analysis above.

Question

A common statistical method for estimating a population size assumes each member of the population has an equal probability of being captured. To assess this assumption for crocodile populations, investigators repeatedly sampled sections of rivers in Australia. Crocodile lengths were measured in size classes. Crocs 0.0 - 0.3 meters in length are in size class 1, 0.3 - 0.6 meters in length are size class 2, etc. The normal maximum adult length is in a class size of 9 or 10. The investigators fit a quadratic function relating the probability of capture and the size class of captured crocodiles. The output from their analysis is shown below.  Polynomial Fit Degree=2
PrCap = 0.66 + 0.77Class − 0.01(Class)^2  ​  ​
(a)What proportion of the variability in probability of capture is explained by the crocodile's size class?
(b)Some biologists speculate that as crocodiles grow they become more wary of humans, and are more difficult to detect in the wild. Support or refute this belief by appealing to the analysis above.

Quizplus · Accepted Answer

The Answer of A common statistical method for estimating a population size assumes each member of the population has an equal probability of being captured. To assess this assumption for crocodile populations, investigators repeatedly sampled sections of rivers in Australia. Crocodile lengths were measured in size classes. Crocs 0.0 - 0.3 meters in length are in size class 1, 0.3 - 0.6 meters in length are size class 2, etc. The normal maximum adult length is in a class size of 9 or 10. The investigators fit a quadratic function relating the probability of capture and the size class of captured crocodiles. The output from their analysis is shown below.  Polynomial Fit Degree=2
PrCap = 0.66 + 0.77Class − 0.01(Class)^2  ​  ​
(a)What proportion of the variability in probability of capture is explained by the crocodile's size class?
(b)Some biologists speculate that as crocodiles grow they become more wary of humans, and are more difficult to detect in the wild. Support or refute this belief by appealing to the analysis above.

A Common Statistical Method for Estimating a Population Size Assumes