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.
$\begin{array} { | c | l | l | l | l | } \hline & { \text { Width (in cm) } } \\\hline \text { Weight } & \begin{array} { l } \text { Tiny } \\\mathbf { 0 - 5 }\end{array} & \begin{array} { l } \text { Small } \\\mathbf { 5 - 1 0 }\end{array} & \begin{array} { l } \text { Medium } \\\mathbf { 1 0 - 1 5 }\end{array} & \begin{array} { l } \text { Large } \\\mathbf { 1 5 - 2 0 }\end{array} \\\hline \text { Light } ( < 1.8 \mathrm {~kg} ) & 39 & 36 & 29 & 18 \\\hline \text { Heavy } ( > 1.8 \mathrm {~kg} ) & 11 & 14 & 21 & 32 \\\hline\end{array}$ The chi-square statistic for these data equals 21.9. What is the P-value for this test?

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.
$$\begin{array} { | c | l | l | l | l | } 
\hline &  { \text { Width (in cm) } } \
\hline \text { Weight } & \begin{array} { l } 
\text { Tiny } \
\mathbf { 0 - 5 }
\end{array} & \begin{array} { l } 
\text { Small } \
\mathbf { 5 - 1 0 }
\end{array} & \begin{array} { l } 
\text { Medium } \
\mathbf { 1 0 - 1 5 }
\end{array} & \begin{array} { l } 
\text { Large } \
\mathbf { 1 5 - 2 0 }
\end{array} \
\hline \text { Light } ( < 1.8 \mathrm {~kg} ) & 39 & 36 & 29 & 18 \
\hline \text { Heavy } ( > 1.8 \mathrm {~kg} ) & 11 & 14 & 21 & 32 \
\hline
\end{array}$$ The chi-square statistic for these data equals 21.9. What is the P-value for this test?

Quizplus · Accepted Answer

Given the chi-square statistic of 21.9, the P-value would be less than 0.01. This is because higher chi-square values typically correspond to lower P-values, indicating a stronger evidence against the null hypothesis in a chi-square test.

A Fisheries Biologist Is Interested in Studying the Relationship Between