91Ó°ÊÓ

In a two-way table, the marginal distribution focuses on one of the categorical variables at a time. It provides the totals for each category, essentially offering a snapshot of one side of the two-way interaction.
For instance, in the context of parental smoking behavior, the marginal distribution would tell us how many students fall under each parental smoking category, regardless of whether the students themselves smoke or not.
To calculate a marginal distribution, you add together entries from a row or a column. In our example, to determine the marginal distribution of parental smoking behavior:

• Sum the students where neither parent smokes: 1168 (not smoking) + 188 (smoking) = 1356.
• Do the same for one parent smoking: 1823 + 416 = 2239.
• For both parents smoking: 1380 + 400 = 1780.

This gives us the counts. To express these as percentages, divide each by the total (5375 students) and multiply by 100 to convert them to percentages.
This way, we identify the part of the whole each category represents, which aids in recognizing overall patterns.

Determining the percent of students who smoke reveals a crucial insight into the student population's behavior. This percentage helps gauge how widespread smoking is among the surveyed students.
First, identify how many students smoke by adding: 188 (neither parent smokes) + 416 (one parent smokes) + 400 (both parents smoke), totaling 1004 smoking students.
Next, calculate the percent of smoking students out of the total student population. Use the formula:\[\text{Percent of smokers} = \left( \frac{1004}{5375} \right) \times 100 \approx 18.68\%\]Such a result, around 18.68%, indicates that a significant portion of students has taken up smoking. This percentage matters, as it could impact school policies, health education, and parental awareness programs.
Knowing this information is not just about numbers, but understanding how many students might need support or intervention.

The two-way table offers insight into how parental smoking behavior might influence student smoking habits. By examining the distribution of students, based on their parents' smoking habits, we gain clues on potential family influences.
Notice that when neither parent smokes, 188 out of 1356 students smoke. However, when one parent smokes, the number increases to 416 out of 2239 students.
If both parents smoke, 400 out of 1780 students also smoke. These frequencies are crucial because they suggest a pattern:

• Environments with one or more parents who smoke correlate with higher student smoking rates.
• The increase in student smokers, moving from one smoking parent to both, reflects possibly stronger influences in homes where both smoke.

These observations highlight the potential impact of parental habits on children. Understanding these patterns can guide interventions and support targeting both students and their families.
By appreciating the influence of parents, educators and policymakers can better focus on creating healthy home environments and reducing smoking rates among youth.