Suppose an ecologist collects data on the weights and basal trunk diameters of a randomly selected sample of felled trees. The ecologist fits a simple linear regression model, predicting tree weight from the trunk's cross-sectional area. After ensuring that all assumptions of the linear model are met, the ecologist computes a 95% confidence interval for the predicted mean weight of trees with a trunk cross-sectional area of 452 in?.
Select the correct interpretation of this confidence interval.

a. The weight of another tree with a trunk cross-sectional area of 452 in- sampled at random from the same population will fall in the ecologist's interval with 95% probability.
b.The true mean weight for trees in the population with a trunk cross-sectional area of 452 in- will fall within the ecologist's interval with 95% probability.
c.The weight of 95% of trees in the population with a trunk cross-sectional area of 452 inwill fall within the ecologist's interval.
d. The ecologist's interval has a 95% chance of containing the true sample mean weight of trees with a trunk cross- sectional area of 452 in².
e. There is a 95% chance that the ecologist's interval contains the true mean weight of trees in the population with a trunk cross-sectional area of 452 in?.

Question

21-12-2019
Mathematics

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Suppose an ecologist collects data on the weights and basal trunk diameters of a randomly selected sample of felled trees. The ecologist fits a simple linear regression model, predicting tree weight from the trunk's cross-sectional area. After ensuring that all assumptions of the linear model are met, the ecologist computes a 95% confidence interval for the predicted mean weight of trees with a trunk cross-sectional area of 452 in?.
Select the correct interpretation of this confidence interval.

a. The weight of another tree with a trunk cross-sectional area of 452 in- sampled at random from the same population will fall in the ecologist's interval with 95% probability.
b.The true mean weight for trees in the population with a trunk cross-sectional area of 452 in- will fall within the ecologist's interval with 95% probability.
c.The weight of 95% of trees in the population with a trunk cross-sectional area of 452 inwill fall within the ecologist's interval.
d. The ecologist's interval has a 95% chance of containing the true sample mean weight of trees with a trunk cross- sectional area of 452 in².
e. There is a 95% chance that the ecologist's interval contains the true mean weight of trees in the population with a trunk cross-sectional area of 452 in?.

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AlonsoDehner AlonsoDehner · Answer 1 · 2019-12-23T06:24:28+01:00

Answer:

e) There is a 95% chance that the ecologist's interval contains the true mean weight of trees in the population with a trunk cross-sectional area of 452 in

Step-by-step explanation:

Given that an ecologist collects data on the weights and basal trunk diameters of a randomly selected sample of felled trees. The ecologist fits a simple linear regression model, predicting tree weight from the trunk's cross-sectional area. After ensuring that all assumptions of the linear model are met, the ecologist computes a 95% confidence interval for the predicted mean weight of trees with a trunk cross-sectional area of 452 inches

We can interpret the confidence interval as

we are 95% confident that for samples of trees largely drawn with 452 inches the mean of these trees would fall within this interval.

e) There is a 95% chance that the ecologist's interval contains the true mean weight of trees in the population with a trunk cross-sectional area of 452 in