A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years is given by 1.272 + 0.570. Assume that the conditions for inference for the slope of the regression equation are met. Which of the following is the correct interpretation of the interval?
A. We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds.
B. We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear's weight of between 7.0 and 18.4 pounds.
C. We are 95 percent confident that for every one-year increase in the age of black bears in the sample, the average increase in the weights of those black bears is between 7.0 and 18.4 pounds.
D. We are 95 percent confident that the mean increase in the age of a black bear for each one-pound increase in the weight of the black bear is between 7.0 and 18.4 years.
E. We are 95 percent confident that any sample of 12 black bears will produce a slope of the regression line between 7.0 and 18.4.

We are 95 percent confident that the mean increase in the weight of a black bear for each one-year increase in the age of the bear is between 7.0 and 18.4 pounds.

Step-by-step explanation:

The 95 confidence interval given by 1.272±0.570, or (0.702,1.842), estimates the relationship between weight in tens of pounds and age in years. So we are 95 percent confident that the mean increase in the weight of a black bear will be between 7.0 and 18.4 pounds for each one-year increase in the age of the bear.

astha8579 astha8579 · Answer 2 · 2022-03-28T09:04:19+02:00

The correct interpretation of the provided confidence interval is given by:

Option B: We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear's weight of between 7.0 and 18.4 pounds.

How to interpret confidence interval?

Suppose the confidence interval at P% for some parameter's values is given by [tex]x \pm y[/tex]

That means, that parameter's estimated value is P% probable to lie in the interval [tex][x - y, x + y][/tex]

For this case, the regression line predicts weight in tens of pounds based on the age in years.

The 95% confidence interval for that prediction is given to be: [tex]1.272 \pm 0.570[/tex]

That means, the predicted value of weight of a black bear (in tens of pounds) when one year age is incremented is 95% probable to lie in the interval [tex][1.272 - 0.57, 1.272 + 0.57] \approx [0.7, 1.84][/tex]

That is for weight in tens of pounds. Converting it to pounds gives us the interval [tex][7.0, 18.4][/tex] approx.

Note the words "prediction", and "of a bear".

That makes us conclude that:

Option B: We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear's weight of between 7.0 and 18.4 pounds.

(focus on the "will result in" phrase. It is taking similar to prediction thing. Since we're taking about regression line which tries to fit line for prediction of future output values for input values, thus, we chose second option.)

Thus, the correct interpretation of the provided confidence interval is given by:

Option B: We are 95 percent confident that an increase of one year in the age of an individual black bear will result in an increase in the black bear's weight of between 7.0 and 18.4 pounds.

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