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?"

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 group of 125 truck owners were asked what brand of truck they owned and whether or not the truck has four-wheel drive. The results are summarized in the two-way table below. Suppose we randomly select one of these truck owners.
$\begin{array}{ccc}& \text{ Four-wheel drive}& \text{ No four-wheel drive }\\ \text{ Ford }& 28& 17\\ \text{ Chevy }& 32& 18\\ \text{ Dodge }& 20& 10\end{array}$
What is the probability that the person owns a Dodge or has four-wheel drive?
$(a)\frac{20}{80}$
$(b)\frac{20}{125}$
$(c)\frac{80}{125}$
$(d)\frac{90}{125}$
$(e)\frac{110}{125}$

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.

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.

In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel.
$\begin{array}{lc}& \text{Class}\\ \text{Survived}& \begin{array}{cccc}& \text{ First }& \text{ Second }& \text{ Third }\\ \text{ Yes }& 197& 94& 151\\ \text{ No }& 122& 167& 476\end{array}\end{array}$
Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P (not a passenger in first class and survived).

The General Social Survey (GSS) asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education:
$\begin{array}{lcccc}& \text{ Associate's }& \text{ Bachelor's }& \text{ Master's }& \text{ Total }\\ \begin{array}{c}\text{ Not al all }\\ \text{ scientific }\end{array}& 169& 256& 114& 539\\ \begin{array}{c}\text{ Very or sort }\\ \text{ of scientific }\end{array}& 65& 65& 18& 148\\ \text{ Total }& 234& 321& 132& 687\end{array}$
State appropriate hypotheses for performing a chi-square test for independence in this setting.

1. Who seems to have more variability in their shoe sizes, men or women?
a) Men
b) Women
c) Neither group show variability
d) Flag this Question
2. In general, why use the estimate of $n-1$ rather than n in the computation of the standard deviation and variance?
a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation
b) The estimate n-1 is never used to calculate the sample variance and standard deviation
c) $n-1$ provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population
d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.
$\begin{array}{|cc|}\hline \text{Shoe Size (in cm)}& \text{Gender (M of F)}\\ 25.7& M\\ 25.4& F\\ 23.8& F\\ 25.4& F\\ 26.7& M\\ 23.8& F\\ 25.4& F\\ 25.4& F\\ 25.7& M\\ 25.7& F\\ 23.5& F\\ 23.1& F\\ 26& M\\ 23.5& F\\ 26.7& F\\ 26& M\\ 23.1& F\\ 25.1& F\\ 27& M\\ 25.4& F\\ 23.5& F\\ 23.8& F\\ 27& M\\ 25.7& F\\ \hline\end{array}$
$\begin{array}{|cc|}\hline \text{Shoe Size (in cm)}& \text{Gender (M of F)}\\ 27.6& M\\ 26.9& F\\ 26& F\\ 28.4& M\\ 23.5& F\\ 27& F\\ 25.1& F\\ 28.4& M\\ 23.1& F\\ 23.8& F\\ 26& F\\ 25.4& M\\ 23.8& F\\ 24.8& M\\ 25.1& F\\ 24.8& F\\ 26& M\\ 25.4& F\\ 26& M\\ 27& M\\ 25.7& F\\ 27& M\\ 23.5& F\\ 29& F\\ \hline\end{array}$