Here are data from a survey conducted at eight high schools...

Here are data from a survey conducted at eight high schools on smoking among students and their parents: ${ }^{17}$ $$ \begin{array}{lccc} \hline & \begin{array}{c} \text { Neither } \\ \text { parent } \\ \text { smokes } \end{array} & \begin{array}{c} \text { One } \\ \text { parent } \\ \text { smokes } \end{array} & \begin{array}{c} \text { Both } \\ \text { parents } \\ \text { smoke } \end{array} \\ \text { Student does not smoke } & 1168 & 1823 & 1380 \\ \text { Student smokes } & 188 & 416 & 400 \\ \hline \end{array} $$ (a) How many students are described in the two-way table? What percent of these students smoke? (b) Give the marginal distribution (in percents) of parents" smoking behavior, both in counts and in percents.

Here are data from a survey conducted at eight high schools on smoking among students and their parents: ${ }^{17}$
$$
\begin{array}{lccc}
\hline & \begin{array}{c}
\text { Neither } \\
\text { parent } \\
\text { smokes }
\end{array} & \begin{array}{c}
\text { One } \\
\text { parent } \\
\text { smokes }
\end{array} & \begin{array}{c}
\text { Both } \\
\text { parents } \\
\text { smoke }
\end{array} \\
\text { Student does not smoke } & 1168 & 1823 & 1380 \\
\text { Student smokes } & 188 & 416 & 400 \\
\hline
\end{array}
$$
(a) How many students are described in the two-way table? What percent of these students smoke?
(b) Give the marginal distribution (in percents) of parents" smoking behavior, both in counts and in percents.

Key Concepts

Survey Data Analysis

Survey data analysis entails the collection, organization, and interpretation of data gathered from surveys. It often uses tools like contingency tables to explore relationships between variables, and calculations such as total counts and percentages help in making inferences about the population being studied.

Percent Calculation

Percent calculations convert raw counts into percentages, allowing for easier interpretation and comparison between groups. The process involves dividing the count of interest by the total number of observations and then multiplying by 100 to achieve a percentage, which is vital for understanding the proportion of students who smoke or the distribution of parental smoking behavior.

Contingency Table

A contingency table displays the frequency distribution of variables. In this context, it organizes data into a two-way table where one categorical variable is the student's smoking behavior and the other is the parent's smoking behavior. This structure allows analysis of the relationship between the two categorical variables by showing counts for each combination of categories.

Marginal Distribution

The marginal distribution involves the totals of the rows or columns in a contingency table, representing the distribution of one variable regardless of the other. In the problem, it is used to summarize the overall counts and percentages for the parent's smoking behavior by summing subjects across all levels of the student's smoking status.

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