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Tail-Feather Length in Birds Is Sometimes a Sexually Dimorphic Trait

Question 5

Multiple Choice

Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of five wild, male long-tailed finches. Here are the data and software output:
 weight (g)  tail length (mm) 20.882.519.182.515.967.016.770.515.773.5\begin{array} { c c } \text { weight } ( \mathrm { g } ) & \text { tail length } ( \mathrm { mm } ) \\20.8 & 82.5 \\19.1 & 82.5 \\15.9 & 67.0 \\16.7 & 70.5 \\15.7 & 73.5\end{array} Simple linear regression results:
Dependent Variable: tail length
Independent Variable: weight
tail length =25.547393+2.8147736= 25.547393 + 2.8147736 weight
Sample size: 5
RR (correlation coefficient ) =0.88813734) = 0.88813734
Rsq=0.78878793\mathrm { R } - \mathrm { sq } = 0.78878793
Estimate of error standard deviation: 3.74116563.7411656

Parameter estimates:

 Parameter  Estimate  Std. Err.  Alternative  DF  T-Stat  P-value  Intercept 25.54739314.928136031.71135850.1855 Slope 2.81477360.84093435033.34719790.0442\begin{array}{|l|c|c|r|r|r|r|}\hline \text { Parameter } & \text { Estimate } & \text { Std. Err. } & \text { Alternative } & \text { DF } & \text { T-Stat } & \text { P-value } \\\hline \text { Intercept } & 25.547393 & 14.928136 & \neq 0 & 3 & 1.7113585 & 0.1855 \\\hline \text { Slope } & 2.8147736 & 0.84093435 & \neq 0 & 3 & 3.3471979 & 0.0442 \\\hline\end{array} What would be the predicted tail-feather length of a male long-tailed finch weighing 30 g?


A) 109.961 mm
B) 78.9 mm
C) We shouldn't make this prediction because the relationship is not linear.
D) We shouldn't make this prediction because it requires extrapolation.

Correct Answer:

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