A Study Examined the Effect of Body Weight and Origin

Multiple Choice

A study examined the effect of body weight and origin (aviary or wild) on the length of the R1 central tail feather in male finches. The following model is proposed for predicting the length of the R1 feather from the bird's weight (in grams) and origin (aviary = 0, wild = 1) :
R1Length_i = β₀ + β₁ (BodyWeight_i) + β₂ (Aviary0Wild1_i) + ε_i
Where the deviations ε_i were assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to a sample of 25 male finches. Using software, we obtained the following output:
$\begin{array} { l r r } \text { Predictor } & \text { Coef } & \text { SE Coef } \\ \text { Constant } & 35.79 & 16.95 \\ \text { BodyWeight } & 2.826 & 1.030 \\ \text { Aviary0Wild1 } & - 10.453 & 4.996 \end{array}$

Predicted Values for New Observations

$\begin{array} { r r r c c } \text { NewObs } & \text { Fit } & \text { SE Fit } & 95 \% \text { CI } & 95 \% \text { PI } \\ 1 & 76.22 & 4.32 & ( 67.26,85.17 ) & ( 54.35,98.09 ) \\ 2 & 86.67 & 2.75 & ( 80.96,92.38 ) & ( 65.91,107.43 ) \end{array}$

Values of Predictors for New Observations

$\begin{array} { c r r } \text { NewObs } & \text { BodyWeight } & \text { Aviary0Wild1 } \\ 1 & 18.0 & 1.0 \\ 2 & 18.0 & 0.0 \end{array}$ What is the best description of the interval (65.91, 107.43) ?

A) A confidence interval for the mean tail-feather length of all male finches that weigh 18 g and are raised in an aviary
B) A confidence interval for the mean tail-feather length of all male finches that weigh 18 g and are caught in the wild
C) A prediction interval for the tail-feather length of one male finch that weighs 18 g and was raised in an aviary
D) A prediction interval for the tail-feather length of one male finch that weighs 18 g and was caught in the wild