Smoking by students and parents Here are data from a survey...

Smoking by students and parents Here are data from a survey conducted at eight high schools on smoking among students and their parents:17
(a) How many students are described in the two-way table? What percent of these students smoke?
(b) Give the marginal distribution of parents’

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Key Concepts

Two-Way Table

A two-way table is a statistical tool used to display the frequency distribution of two categorical variables simultaneously. It organizes data into rows and columns that represent the categories of the variables, which helps to examine potential relationships or associations between those variables.

Marginal Distribution

The marginal distribution represents the totals for each category of one variable, regardless of the other variable. It is obtained by summing the corresponding rows or columns in a two-way table, and it provides an overall picture of how the data is distributed for a single variable.

Percentage Calculation

Percentage calculation involves determining the proportion of a particular subset relative to the total and then multiplying by 100. This concept is essential when analyzing survey data as it allows for a standardized comparison of different groups even when the overall sample sizes vary.

Contingency Table Analysis

Contingency table analysis is a statistical method used to explore the relationship between two categorical variables by organizing the data into a matrix format. It aids in assessing whether an association exists between the variables by comparing observed frequencies with what might be expected under independence.

Transcript

00:01 For question 20, we're given a two -way table that includes data on the smoking habits of students as well as their parents.

00:07 So there's two variables.

00:08 One is the smoking status of the student.

00:13 So students may not smoke or they may smoke.

00:18 And the other variable is the status of smoking for their parents.

00:22 So for each student, you may have neither parent that is a smoker or one or both.

00:33 And so the data from the question are these here.

00:49 And part a asked, what are the total number of students represented by the table? as always with a two -way table, good starting point is to sum the rows and the columns.

01:00 So if we sum the rows, the first row gives us 4 ,371, 1004 for the second row.

01:11 The first column gives us 1 ,356.

01:22 And then if you sum either of the last column or the bottom row, it gives you 5 ,375.

01:34 So once you've sum the rows and the columns, this bottom right cell is always the total number of individuals represented by the table.

01:43 So for part a, the first part of the answer is 5 ,375 students are represented by the table.

01:50 And the second part of part a is to give the percent of students who do smoke.

01:55 So that is, by definition, this row here...

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