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 5 wild male long-tailed finches. Here are the data:
$\begin{array} { c c } \text { weight } ( \mathrm { g } ) & \text { tail length } ( \mathrm { mm } ) \\20.8 & 82.5 \\19.1 & 82.5 \\15.9 & 67.0 \\16.7 & 70.5 \\15.7 & 73.5\end{array}$ We want to test the hypotheses H₀: β= 0, versus H_a: β> 0, where βis the true value of the population slope. Using appropriate software, what is the value of the t statistic for this test?

Question

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 5 wild male long-tailed finches. Here are the data:

\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}

We want to test the hypotheses H₀: β= 0, versus H_a: β> 0, where βis the true value of the population slope. Using appropriate software, what is the value of the t statistic for this test?

Quizplus · Accepted Answer

Using appropriate software, the t statistic for testing H₀: β= 0, versus H_a: β> 0, where βis the true value of the population slope, is found to be 3.34.

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