Tail-feather length in birds is sometimes a sexually dimorphic trait; that is, the trait differs substantially for males and for females of the same species. Researchers studied the relationship between tail-feather length (measuring the R1 central tail feather) and weight in a sample of 20 male long-tailed finches raised in an aviary. The data are displayed in the scatterplot below, followed with software output about the least-squares regression model of feather length as a function of weight. $$\begin{array}{l} \begin{array} { l l r } \hline &\text {Coefficients }&\text {Standard Error }\ \hline\text {Intercept }&35.7379 & 21.0523 \ \text { Bird-weight}&2.8299 & 1.2811\ \hline\text {R Square }&0.2133\ \text {Standard Error }&\ 10.5270\ \end{array} \end{array}$$ We want to test the hypotheses H₀: β = 0 versus H_a: β 0, where β is the true value of the population slope. What is the P-value 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 of the same species. Researchers studied the relationship between tail-feather length (measuring the R1 central tail feather) and weight in a sample of 20 male long-tailed finches raised in an aviary. The data are displayed in the scatterplot below, followed with software output about the least-squares regression model of feather length as a function of weight. $$\begin{array}{l} \begin{array} { l l r } \hline &\text {Coefficients }&\text {Standard Error }\ \hline\text {Intercept }&35.7379 & 21.0523 \ \text { Bird-weight}&2.8299 & 1.2811\ \hline\text {R Square }&0.2133\ \text {Standard Error }&\ 10.5270\ \end{array} \end{array}$$ We want to test the hypotheses H₀: β = 0 versus H_a: β > 0, where β is the true value of the population slope. What is the P-value for this test?

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The Answer of Tail-feather length in birds is sometimes a sexually dimorphic trait; that is, the trait differs substantially for males and for females of the same species. Researchers studied the relationship between tail-feather length (measuring the R1 central tail feather) and weight in a sample of 20 male long-tailed finches raised in an aviary. The data are displayed in the scatterplot below, followed with software output about the least-squares regression model of feather length as a function of weight. $$\begin{array}{l} \begin{array} { l l r } \hline &\text {Coefficients }&\text {Standard Error }\ \hline\text {Intercept }&35.7379 & 21.0523 \ \text { Bird-weight}&2.8299 & 1.2811\ \hline\text {R Square }&0.2133\ \text {Standard Error }&\ 10.5270\ \end{array} \end{array}$$ We want to test the hypotheses H₀: β = 0 versus H_a: β > 0, where β is the true value of the population slope. What is the P-value for this test?

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