# 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. begin{array}{l|c|c|c} & Married & Not married & Total hline Own & 172 & 82 & 254 hline Rent & 40 & 54 & 94 hline Total & 212 & 136 & 348 end{array} State the hypotheses for a test of the relationship between marital status and housing status for U.S. residents.

Question
Two-way tables
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.

2021-01-20
Given: $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{c}{\mid}{c}\right\rbrace}&{M}{a}{r}{r}{i}{e}{d}&{N}{o}{t}{m}{a}{r}{r}{i}{e}{d}&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{O}{w}{n}&{172}&{82}&{254}\backslash{h}{l}\in{e}{R}{e}{n}{t}&{40}&{54}&{94}\backslash{h}{l}\in{e}{T}{o}{t}{a}{l}&{212}&{136}&{348}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ The null hypothesis states that there is no association between the variables. The alternative hypothesis states that there is an association between the variables. $$\displaystyle{H}_{{0}}$$: There is no association between marital status and housing status. $$\displaystyle{H}_{{a}}$$ : There is an association between marital status and housing status.

### Relevant Questions

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. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{c}{\mid}{c}\right\rbrace}&{M}{a}{r}{r}{i}{e}{d}&{N}{o}{t}{m}{a}{r}{r}{i}{e}{d}&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{O}{w}{n}&{172}&{82}&{254}\backslash{h}{l}\in{e}{R}{e}{n}{t}&{40}&{54}&{94}\backslash{h}{l}\in{e}{T}{o}{t}{a}{l}&{212}&{136}&{348}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
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.
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.
The Pew Research Center asked a random sample of 2024 adult cellphone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). The two-way table summarizes the data.
$$\begin{array}{c|ccc|c} & 18-34 & 35-54 & 55+ & \text { Total } \\ \hline \text { iPhone } & 169 & 171 & 127 & 467 \\ \text { Androod } & 214 & 189 & 100 & 503 \\ \text { Other } & 134 & 277 & 643 & 1054 \\ \hline \text { Total } & 517 & 637 & 870 & 2024 \end{array}$$
Suppose we select one of the survey respondents at random. What's the probability that: The person is not age 18 to 34 and does not own an iPhone?
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}\)
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?
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. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{c}\right\rbrace}&{F}{e}{m}{a}\le&{M}{a}\le\backslash{h}{l}\in{e}{A}{b}{o}{u}{t}{r}{i}{g}{h}{t}&{560}&{295}\backslash{h}{l}\in{e}{O}{v}{e}{r}{w}{e}{i}{g}{h}{t}&{163}&{72}\backslash{h}{l}\in{e}{U}{n}{d}{e}{n}{v}{e}{i}{g}{h}{t}&{37}&{73}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$
$$\begin{array}{c|c} & Female\ \ \ \ \ \ Male & Total \\ \hline About\ right & 560\ \ \ \ \ \ \ \ \ \ 295 & 855\\ \hline Overweight & 163\ \ \ \ \ \ \ \ \ \ 72 & 235 \\ \hline Underweight & 37\ \ \ \ \ \ \ \ \ \ \ \ 73 & 110 \\ \hline Total & 760\ \ \ \ \ \ \ \ \ \ 440 & 1200 \end{array}$$
$$\begin{array} {c|cc|c} & \text { Female } & \text { Male } & \text { Total } \\ \hline \text { Almost no chance } & 96 & 98 & 194 \\ \hline \text { Some chance but probably not } & 426 & 286 & 712 \\ \hline \text { A 50-50 chance } & 696 & 720 & 1416 \\ \hline \text { A good chance } & 663 & 758 & 1421 \\ \hline \text { Almost certain } & 486 & 597 & 1083 \\ \hline \text { Total } & 2367 & 2459 & 4826 \end{array}$$