A fisheries biologist is interested in studying the relationship between width and weight in horseshoe crabs. She collects a simple random sample of such crabs and cross-classifies them based on these variables as given below.
$\begin{array} { | c | l | l | l | l | } \hline & & { \text { Width (in cm) } } \\\hline \hline \text { Weight } & \begin{array} { l } \text { Tiny } \\\mathbf { 0 - 5 }\end{array} & \begin{array} { l } \text { Small } \\\mathbf { 5 - 1 0 }\end{array} & \begin{array} { l } \text { Medium } \\\mathbf { 1 0 - 1 5 }\end{array} & \begin{array} { l } \text { Large } \\\mathbf { 1 5 - 2 0 }\end{array} \\\hline \text { Light } ( < 1.8 \mathrm {~kg} ) & 39 & 36 & 29 & 18 \\\hline \text { Heavy } ( > 1.8 \mathrm {~kg} ) & 11 & 14 & 21 & 32 \\\hline\end{array}$ To compare the four classes of widths with respect to weight, which distribution should we calculate?

Question

A fisheries biologist is interested in studying the relationship between width and weight in horseshoe crabs. She collects a simple random sample of such crabs and cross-classifies them based on these variables as given below.
$$\begin{array} { | c | l | l | l | l | } 
\hline & & { \text { Width (in cm) } } \
\hline \hline \text { Weight } & \begin{array} { l } 
\text { Tiny } \
\mathbf { 0 - 5 }
\end{array} & \begin{array} { l } 
\text { Small } \
\mathbf { 5 - 1 0 }
\end{array} & \begin{array} { l } 
\text { Medium } \
\mathbf { 1 0 - 1 5 }
\end{array} & \begin{array} { l } 
\text { Large } \
\mathbf { 1 5 - 2 0 }
\end{array} \
\hline \text { Light } ( < 1.8 \mathrm {~kg} ) & 39 & 36 & 29 & 18 \
\hline \text { Heavy } ( > 1.8 \mathrm {~kg} ) & 11 & 14 & 21 & 32 \
\hline
\end{array}$$ To compare the four classes of widths with respect to weight, which distribution should we calculate?

Quizplus · Accepted Answer

To compare the four classes of widths with respect to weight, calculating the conditional distribution of weight given width is appropriate. This allows for understanding how weight distribution changes across different width categories.

A Fisheries Biologist Is Interested in Studying the Relationship Between