Master Two Way Tables with Our Expert Answers

You randomly survey students in your school about whether they liked a recent school play. The two-way table shows the results. Find and interpret the marginal frequencies.

$\begin{array}{|ccc|}\hline & & \text{Student}\\ & & \text{Liked}& \text{Did Not like}\\ \text{Gender}& \text{Male}& 48& 12\\ & \text{Female}& 56& 14\\ \hline\end{array}$

A random sample of 1200 U.S. college students was asked, "What is your perception of your own body? Do you feel that you are overweight, underweight, or about right?" The two-way table summarizes the data on perceived body image by gender.$\begin{array}{cc}& \text{Gender}\\ \text{Body image}& \begin{array}{lccr}& \text{ Female }& \text{ Male }& \text{ Total }\\ \text{ About right }& 560& 295& 855\\ \text{ Overwerght }& 163& 72& 235\\ \text{ Underweight }& 37& 73& 110\\ \text{ Total }& 760& 440& 1200\end{array}\end{array}$What percent of respondents are males and feel that they are overweight or underweight?

Here are the row and column totals for a two-way table with two rows and two columns:$\begin{array}{llr}a& b& 50\\ c& d& 50\\ 60& 40& 100\end{array}$ Find two different sets of counts a, b, c, and d for the body of the table that give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.

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 study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-50s.

$\begin{array}{lc}& \text{Soccer experience}\\ \text{Arthritis}& \begin{array}{lcccc}& & & \text{ Did not }& \\ & \text{ Elite }& \text{ Non-elite }& \text{ play }& \text{ Total }\\ \text{ Yes }& 10& 9& 24& 43\\ \text{ No }& 61& 206& 548& 815\\ \text{ Total }& 71& 215& 572& 858\end{array}\end{array}$

Suppose we choose one of these players at random. What is the probability that the player has arthritis?

A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-fifties: $$\begin{gathered} \text{Soccer level} \\ \begin{array}{llccc}& & \text{ Ellte }& \text{ Non-elite }& \text{ Did not play }\\ \text{ Whether person }& \text{ Yes }& 10& 9& 24\\ \text{ developed arthritis }& \text{ No }& 61& 206& 548\end{array} \end{gathered}$$ Researchers suspected that the more serious soccer players were more likely to develop arthritis later in life. Do the data confirm this suspicion? Calculate appropriate percentages to support your answer.

A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-50s.

$\begin{array}{ccccc}& \text{ Elite }& \text{ Non-elite }& \text{Did not play }& \text{ Total }\\ \text{ Yes }& 10& 9& 24& 43\\ \text{ No }& 61& 206& 548& 815\\ \text{ Total }& 71& 215& 572& 858\end{array}$
Suppose we choose one of these players at random. What is the probability that the player has arthritis, given that he or she was classified as an elite soccer player?

The Pew Research Center polled a random sample of 2024 American adult cellphone owners to find out their age and if they own an iPhone, an Android, or something else (including non-smartphones). The data are summarized in the two-way table.
$\begin{array}{ccccc} & 18-34& 35-54& 55+& \text{ Total }\\ \text{ iPhone }& 169& 171& 127& 467\\ \text{ Androod }& 214& 189& 100& 503\\ \text{ Other }& 134& 277& 643& 1054\\ \text{ Total }& 517& 637& 870& 2024\end{array}$
Let's say we choose one of the survey participants at random. What is the chance that the person is not between the ages of 18 and 34 and doesn't have an iPhone?