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 21 g). Using software, we obtain the following output for predicting feather length when weight = 20 g: $$\begin{array} { r r r c c }
\text { New Obs } & \text { Fit } & \text { SE Fit } & 95 \% \text { CI } & 95 \% \text { PI } \
20.0 & 92.34 & 5.26 & ( 81.29,103.38 ) & ( 67.61,117.06 )
\end{array}$$ What is a 95% prediction interval for the weight of one male long-tailed finch weighing 20 g?

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 21 g). Using software, we obtain the following output for predicting feather length when weight = 20 g: $$\begin{array} { r r r c c } 
\text { New Obs } & \text { Fit } & \text { SE Fit } & 95 \% \text { CI } & 95 \% \text { PI } \
20.0 & 92.34 & 5.26 & ( 81.29,103.38 ) & ( 67.61,117.06 )
\end{array}$$ What is a 95% prediction interval for the weight of one male long-tailed finch weighing 20 g?

Quizplus · Accepted Answer

The 95% prediction interval for the weight of one male long-tailed finch weighing 20 g is given as (67.61, 117.06), which is calculated from the center value (Fit = 92.34) by adding and subtracting the range to get the interval. The range is half the difference between 117.06 and 67.61, which is approximately 24.72. Therefore, the correct prediction interval is 92.34 ± 24.72.

Researchers Found a Linear Relationship Between Tail-Feather Length (In Mm)