The two-way table summarizes information about eye color and gender in a random sample of 200 high school students.

The two-way table summarizes data on whether students at a certain high school eat regularly in the school cafeteria by grade level.

$\text{Grade}\text{Eat in cafeteria}\begin{array}{lrrrrr}& 9\mathrm{th}& 10\mathrm{th}& 11\mathrm{th}& 12\mathrm{th}& \text{ Total }\\ \text{ Yes }& 130& 175& 122& 68& 495\\ \text{ No }& 18& 34& 88& 170& 310\\ \text{ Total }& 148& 209& 210& 238& 805\end{array}$

If you choose a student at random who eats regularly in the cafeteria, what is the probability that the student is a 10th-grader?

A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do you think are the chances you will have much more than a middle-class income at age 30?" The two-way table summarizes the responses.
$\begin{array}{cccc}& \text{ Female }& \text{ Male }& \text{ Total }\\ \text{ Almost no chance }& 96& 98& 194\\ \text{ Some chance but }\text{ probably not }& 426& 286& 712\\ \text{ A 50-50 chance }& 696& 720& 1416\\ \text{ A good chance }& 663& 758& 1421\\ \text{ Almost certain }& 486& 597& 1083\\ \text{ Total }& 2367& 2459& 4826\end{array}$
Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Find $P(C\mid M)$. Interpret this value in context.

Physical therapy (PT) may be just as successful as traditional surgery when treating a specific type of knee ligament tear in elderly patients. A group of researchers at a large teaching hospital conduct a trial in which patients are randomly assigned to one of three treatments. A "success" means that the subject had regained full range of motion in their knee 6 months post- treatment.
$\begin{array}{|ccc|}\hline & \text{ Success }& \text{ Failure }\\ \text{ Surgery }& 56& 22\\ \text{ PT }& 54& 35\\ \text{ Surgery+PT }& 85& 18\\ \hline\end{array}$
When analyzing their data, which test would be appropriate for these researchers to use?
Chi-square test of/for $\square$