Smoking by students and parents Refer to Exercise 20....

Name: Problem 22, Chapter 1: The Practice of Statistics for AP
Uploaded: 2020-05-02T04:08:16-08:00
Duration: 5 min 5 s
Channel: Robin Corrigan
Description: Smoking by students and parents Refer to Exercise 20. Calculate three conditional distributions of students’ smoking behavior: one for each of the three parental smoking categories. Describe the relationship between the smoking behaviors of students and their parents in a few sentences.

Smoking by students and parents Refer to Exercise 20. Calculate three conditional distributions of students’ smoking behavior: one for each of the three parental smoking categories. Describe the relationship between the smoking behaviors of students and their parents in a few sentences.

Key Concepts

Categorical Data Analysis

Categorical data analysis involves methods used to analyze data where the variables are categories rather than numerical values. In this problem, it involves calculating probabilities based on count data and assessing how these categorical outcomes relate to one another across different groups.

Association Between Variables

Analyzing the conditional distributions helps in understanding the potential association between students' and parents' smoking behaviors. By comparing the distributions, one can identify whether a change in the parental smoking category is linked to a corresponding change in student behavior.

Conditional Distribution

A conditional distribution describes the probability of different outcomes of one variable given that another variable is held fixed. In this context, it is the distribution of students' smoking behaviors within each category of parental smoking, providing insights into how student behavior changes with different parental influences.

Contingency Table

A contingency table is a matrix format used to display the frequency distribution of variables. It allows us to organize and compare the counts of smoking behaviors among students across different parental smoking categories, making it easier to compute and visualize conditional distributions.

Transcript

00:01 For question 22, we're asked to refer back to a two -way table from question 20, which was about student's smoking behavior along with their parents ' smoking behavior.

00:10 And so i've reproduced that table here, and i've also reproduced the row and column sums that we had generated as part of that question.

00:18 In this question, we're asked to provide the conditional distribution of students ' smoking behavior for each of the categories of parents ' smoking behavior.

00:27 That is, we want to provide the student's conditional distribution conditioned on each of students having neither parent as a smoker, students having one parent as a smoker, or students having both parents as a smoker.

00:41 So just to illustrate that a little bit better, so these categories of no and yes, we can say they're categories of a variable.

00:51 We can call that student smoking behavior.

01:02 And likewise with neither one or both, these categories are part of a variable.

01:07 We can call that parents ' smoking behavior.

01:16 So that's why it's a two -way table.

01:18 We have two variables, and both of these variables have their own categories.

01:24 So the conditional distribution of students smoking, based on students only who have neither parent as a smoker, is highlighted in yellow.

01:35 So that is, if we look at the distribution of students smoking, so yes or no, thinking, only of students who have neither parent as a smoker, the breakdown is 1168 are non -smokers, and 188 of the students are smokers.

01:53 And then if we condition students smoking on only students who have one parent as a smoker, we get this distribution.

02:01 The conditional distribution of student smoking behavior for students who have both parents as a smoker is this column.

02:10 So those three different columns are the three distributions.

02:14 Of students smoking conditioned on the categories of parents of smoking.

02:20 So that is pretty much the three conditional distributions.

02:23 Now it's always most illustrative to put those in terms of percents.

02:28 So we might want to convert those to percents.

02:30 So let's start with a title, so we'll say for the neither category.

02:38 So as expected, we'll break it down by knowing yes...