Skip to main content
Ch. 12 - Analysis of Variance
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 12 - Analysis of VarianceProblem 12.Q.9a
Chapter 12, Problem 12.Q.9a

"Interaction
a. Based on the display included with the preceding exercise, what do you conclude about an interaction between gender and age bracket?

Verified step by step guidance
1
Step 1: Understand what an interaction means in the context of two categorical variables, such as gender and age bracket. An interaction occurs when the effect of one variable on the outcome depends on the level of the other variable.
Step 2: Review the display (such as a table or graph) that shows the relationship between gender, age bracket, and the outcome variable. Look for patterns where the difference between genders changes across different age brackets.
Step 3: Identify if the lines or bars representing different genders cross or diverge significantly across age brackets. Crossing lines or varying gaps suggest an interaction effect.
Step 4: Formulate your conclusion by stating whether the effect of gender on the outcome varies by age bracket (interaction present) or if the effect of gender is consistent across all age brackets (no interaction).
Step 5: Support your conclusion by referencing specific parts of the display that illustrate the presence or absence of interaction, such as differences in means or proportions that change with age bracket.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Interaction Effect

An interaction effect occurs when the effect of one independent variable on the dependent variable differs depending on the level of another independent variable. In this case, it means the relationship between gender and the outcome changes across different age brackets, indicating that gender and age do not act independently.
Recommended video:
03:33
Finding Binomial Probabilities Using TI-84 Example 1

Factorial Design

A factorial design involves studying two or more independent variables simultaneously to observe their individual and combined effects on a dependent variable. Understanding this design helps interpret how gender and age bracket together influence the outcome, including any interaction effects.
Recommended video:
05:22
Combinations

Interpreting Interaction Plots

Interaction plots graphically display how the levels of one factor affect the outcome at different levels of another factor. By examining the lines for gender across age brackets, one can determine if they cross or diverge, which signals the presence and nature of an interaction.
Recommended video:
Guided course
07:38
Residuals and Residual Plots
Related Practice
Textbook Question

Win 4 Lottery Shown below is a histogram of digits selected in California’s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.


c. Identify the frequencies, then test the claim that the digits are selected from a population in which the digits are all equally likely. Is there a problem with the lottery?


Textbook Question

One vs. Two What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?

Textbook Question

Interaction

b. If there does appear to be an interaction between gender and age bracket, how should we continue with the procedure for two-way analysis of variance?

Textbook Question

Win 4 Lottery Shown below is a histogram of digits selected in California’s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.


b. Does the display depict a normal distribution? Why or why not? What should be the shape of the histogram?


Textbook Question

Gender and Age Bracket Based on the display included with Exercise 8, what are the final conclusions?

1
views
Textbook Question

In Exercises 1–5, refer to the following list of numbers of years that deceased U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing, the last president is George H. W. Bush, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples from larger populations.


[Image]


Exploring the Data Include appropriate units in all answers.


e. What is the level of measurement of the data (nominal, ordinal, interval, ratio)?

1
views