# 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}{c|c} & Female Male & Total hline About right & 560 295 & 855 hline Overweight & 163 72 & 235 hline Underweight & 37 73 & 110 hline Total & 760 440 & 1200 end{array} What proportion of the sample is female?

Question
Two-way tables
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.
$$\begin{array}{c|c} & Female\ \ \ \ \ \ Male & Total \\ \hline About\ right & 560\ \ \ \ \ \ \ \ \ \ 295 & 855\\ \hline Overweight & 163\ \ \ \ \ \ \ \ \ \ 72 & 235 \\ \hline Underweight & 37\ \ \ \ \ \ \ \ \ \ \ \ 73 & 110 \\ \hline Total & 760\ \ \ \ \ \ \ \ \ \ 440 & 1200 \end{array}$$
What proportion of the sample is female?

2021-02-13
The study includes 1200 U.S. college students.
$$\begin{array}{c|c} & Female\ \ \ \ \ \ Male & Total \\ \hline About\ right & 560\ \ \ \ \ \ \ \ \ \ 295 & 855\\ \hline Overweight & 163\ \ \ \ \ \ \ \ \ \ 72 & 235 \\ \hline Underweight & 37\ \ \ \ \ \ \ \ \ \ \ \ 73 & 110 \\ \hline Total & 760\ \ \ \ \ \ \ \ \ \ 440 & 1200 \end{array}$$
We then note that 760 of the 1200 U.S. college students are female (as 760 is mentioned in the row ”Total” and in the column ”Female” of the table). $$\frac{760}{1200}=\frac{19}{30}\approx0.6333=63.33\%$$ Thus approximately 0.6333 of the respondents are female. Result 0.6333

### Relevant Questions

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 below summarizes the data on perceived body image by gender. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{c}\right\rbrace}&{F}{e}{m}{a}\le&{M}{a}\le\backslash{h}{l}\in{e}{A}{b}{o}{u}{t}{r}{i}{g}{h}{t}&{560}&{295}\backslash{h}{l}\in{e}{O}{v}{e}{r}{w}{e}{i}{g}{h}{t}&{163}&{72}\backslash{h}{l}\in{e}{U}{n}{d}{e}{n}{v}{e}{i}{g}{h}{t}&{37}&{73}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
A random sample of 88 U.S. 11th- and 12th-graders was selected. The two-way table summarizes the gender of the students and their response to the question "Do you have allergies?" Suppose we choose a student from this group at random.
$$\begin{array}{c|cc|c} & \text { Female } & \text { Male } & \text { Total } \\ \hline \text{ Yes } & 19 & 15 & 34 \\ \text{ No } & 24 & 30 & 54 \\ \hline \text{ Total } & 43 & 45 & 88\\ \end{array}\$$
What is the probability that the student is female or has allergies?
$$(a)\frac{19}{88}$$
(b)\frac{39}{88}\)
(c)\frac{58}{88}\)
(d)\frac{77}{88}\)
The two-way table summarizes data on the gender and eye color of students in a college statistics class. Imagine choosing a student from the class at random. Define event A: student is male and event B: student has blue eyes.
$$\begin{array}{c|cc|c} &\text{Male}&\text{Female}&\text{Total}\\ \hline \text{Blue}&&&10\\ \text{Brown}&&&40\\ \hline \text{Total}&20&30&50 \end{array}\$$
Copy and complete the two-way table so that events A and B are mutually exclusive.
Is there a relationship between gender and relative finger length? To find out, we randomly selected 452 U.S. high school students who completed a survey. The two-way table summarizes the relationship between gender and which finger was longer on the left hand (index finger or ring finger).
$$\begin{array} {lc} & \text{Gender} \ \text {Longer finger} & \begin{array}{l|c|r|r} & \text { Female } & \text { Male } & \text { Total } \\\hline \text { Index finger } & 78 & 45 & 123 \\\hline \text{ Ring finger } & 82 & 152 & 234 \\ \hline \text { Same length } & 52 & 43 & 95 \\ \hline \text { Total } & 212 & 240 & 452 \end{array}\ \end{array}$$
Suppose we randomly select one of the survey respondents. Define events R: ring finger longer and F: female. Given that the chosen student does not have a longer ring finger, what's the probability that this person is male? Write your answer as a probability statement using correct symbols for the events.
A survey of 4826 randomly selected young adults (aged 19 to 25 ) asked, "What do you think are the chances you will have much more than a middle-class income at age 30? The two-way table summarizes the responses.
$$\begin{array} {c|cc|c} & \text { Female } & \text { Male } & \text { Total } \\ \hline \text { Almost no chance } & 96 & 98 & 194 \\ \hline \text { Some chance but probably not } & 426 & 286 & 712 \\ \hline \text { A 50-50 chance } & 696 & 720 & 1416 \\ \hline \text { A good chance } & 663 & 758 & 1421 \\ \hline \text { Almost certain } & 486 & 597 & 1083 \\ \hline \text { Total } & 2367 & 2459 & 4826 \end{array}$$
Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Given that the chosen student didn't say "almost no chance," what's the probability that this person is female? Write your answer as a probability statement using correct symbols for the events.
A random sample of U.S. adults was recently asked, "Would you support or oppose major new spending by the federal government that would help undergraduates pay tuition at public colleges without needing loans?" The two-way table shows the responses, grouped by age. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\mathcal{{c}}}\right\rbrace}&{A}\ge\ {R}{e}{s}{p}{o}{n}{s}{e}&{\left\lbrace{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{r}\right|}{r}{\left|{r}\right|}{r}{\mid}{r}\right\rbrace}&{18}-{34}&{35}-{49}&{50}-{64}&{65}+&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{S}{u}{p}{p}{\quad\text{or}\quad}{t}&{91}&{161}&{272}&{332}&{856}\backslash{h}{l}\in{e}{O}{p}{p}{o}{s}{e}&{25}&{74}&{211}&{255}&{565}\backslash{h}{l}\in{e}{D}{o}{n}'{t}{k}{n}{o}{w}&{4}&{13}&{20}&{51}&{88}\backslash{h}{l}\in{e}{T}{o}{t}{a}{l}&{120}&{248}&{503}&{638}&{1509}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\right\rbrace}\ {e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ Do these data provide convincing evidence of an association between age and opinion about loan-free tuition in the population of U.S. adults?
Is there a relationship between gender and relative finger length? To find out, we randomly selected 452 U.S. high school students who completed a survey. The two-way table summarizes the relationship between gender and which finger was longer on the left hand (index finger or ring finger). $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{c}\right\rbrace}&\text{Gender}\backslash\text{Longer finger}&{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{r}{\mid}{r}\right\rbrace}&\ \text{ Female }\ &\ \text{ Male }\ &\ \text{ Total }\ \backslash{h}{l}\in{e}\ \text{ Index finger }\ &{78}&{45}&{123}\backslash{h}{l}\in{e}\ \text{ Ring finger }\ &{82}&{152}&{234}\backslash{h}{l}\in{e}\ \text{ Same length }\ &{52}&{43}&{95}\backslash{h}{l}\in{e}\ \text{ Total }\ &{212}&{240}&{452}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\backslash{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ Suppose we randomly select one of the survey respondents. Define events R: ring finger longer and F: female. Find P(R|F). Interpret this value in context.
$$\begin{array}{c|cc|c} &\text { Female } & \text { Male } & \text { Total } \\ \hline \text { Almost no chance } & 96 & 98 & 194 \\ \hline \text { Some chance but } \ \text { probably not } & 426 & 286 & 712 \\\hline \text { A 50-50 chance } & 696 & 720 & 1416 \\ \hline \text { A good chance } & 663 & 758 & 1421 \\ \hline \text { Almost certain } & 486 & 597 & 1083 \\ \hline \text { Total } & 2367 & 2459 & 4826 \end{array}$$
Using data from the 2000 census, a random sample of 348 U.S. residents aged 18 and older was selected. The two-way table summarizes the relationship between marital status and housing status for these residents. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{c}{\mid}{c}\right\rbrace}&{M}{a}{r}{r}{i}{e}{d}&{N}{o}{t}{m}{a}{r}{r}{i}{e}{d}&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{O}{w}{n}&{172}&{82}&{254}\backslash{h}{l}\in{e}{R}{e}{n}{t}&{40}&{54}&{94}\backslash{h}{l}\in{e}{T}{o}{t}{a}{l}&{212}&{136}&{348}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ State the hypotheses for a test of the relationship between marital status and housing status for U.S. residents.