Question

Researchers found a linear relationship between tail-feather length (in mm) and weight (in g) in a random sample of 20 male long-tailed finches raised in an aviary (with weights ranging from about 13 to 21g). Using software, we obtain the following output for predicting feather length when weight = 20g. What is a 95 % confidence interval for the mean weight of male long-tailed finches weighing 20g?

Answer 1

Explanation:

As far as I know, this question is not correct. I have the searched the internet and found a similar question which makes sense. In the correct question, 95% Confidence Interval is already given calculated from the software and

95% prediction interval is asked (PI) for the weight of one male long tailed finch weighing 20 g.

We have this data given in the correct question found on internet. And they have calculated this data using software:

New Obs = 20

Fit = 92.34

SE Fit = 5.26

95% Confidence Interval = (81.29, 103.38)

95% Prediction Interval = (67.61, 117.06)

Now, Just look at the prediction interval:

Now the formula for Prediction Interval = Point Estimate ± Margin of Error

Upper limit for prediction interval = 117.06

lower limit = 67.61

Formula for point estimate = (Upper + Lower)/2

Point Estimate = (117.06 + 67.61)/2

Point Estimate = 92.34

Formula for margin of error = (Upper - Lower)/2

Margin of Error = (117.06 - 67.61)/2

Margin of Error = 24.72

Formula for Prediction Interval = Point Estimate ± Margin of Error

PI = 92.34 ± 24.72