A Fisheries Biologist Is Interested in Studying the Relationship Between

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.
$$\begin{array} { | c | l | l | l | l | } \hline & { \text { Width (in cm) } } \\\hline \hline \text { Weight } & \begin{array} { l } \text { Tiny } \\\mathbf { 0 - 5 }\end{array} & \begin{array} { l } \text { Small } \\\mathbf { 5 - 1 0 }\end{array} & \begin{array} { l } \text { Medium } \\\mathbf { 1 0 - 1 5 }\end{array} & \begin{array} { l } \text { Large } \\\mathbf { 1 5 - 2 0 }\end{array} \\\hline \text { Light } ( < 1.8 \mathrm {~kg} ) & 39 & 36 & 29 & 18 \\\hline \text { Heavy } ( > 1.8 \mathrm {~kg} ) & 11 & 14 & 21 & 32 \\\hline\end{array}$$ Which hypotheses are being tested by the chi-square test?

A) The null hypothesis is that width and weight are independent, and the alternative hypothesis is that they are dependent.
B) The null hypothesis is that the mean number of crabs that are in the low-weight class is the same for each of the four width classes, and the alternative hypothesis is that these means are different.
C) The null hypothesis is that the distributions of the number of crabs that are in the low- and high-weight classes are the same for the four widths; the alternative hypothesis says the distributions are different.
D) The null hypothesis is that the distributions of the total number of crabs sampled in each of the four widths are the same; the alternative hypothesis is that these distributions are different.