A researcher conducted an experiment to test the effects of running 3 different types of gasoline with 3 possible types of additive on the mileage obtained. The experiment assumed that there is an interaction between gasoline type and the type of additive, hence, a two-factor ANOVA was employed in the data analysis. It was decided to run 36 motors – 4 in each factor level combinations. The following are the analysis results MEAN   ADDITIVE 1 ADDITIVE 2 ADDITIVE 3   GAS TYPE 1 125.825  130.775 128.275 128.2917 GAS TYPE 2 127 133.6 137.825 132.8083 GAS TYPE 3 126.35 132.5 123 127.2833   126.3917 132.2917 129.7 129.4611 Analysis of Variance Table   Df Sum Sq Mean Sq F Value Pr(>F) factor(gas.type) 2 207.7706 103.8853 11.08482 0.000306 factor(additive)  2 209.8872 104.9436 11.19775 0.000287 factor(gas.type):factor(additive)  4 262.9678 65.74194 7.01483 0.000523 Residuals 27 253.04 9.371852 NA NA a.) Is there a significant interaction between the type of gasoline and the type of additive? Why? b.) What does the result on the test for significant interaction imply? c.) Say you are to choose between the three gasoline types, regardless of the type of additive used and considering all other factors constant. Which gasoline would you prefer for your motor and why?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

A researcher conducted an experiment to test the effects of running 3 different types of gasoline with 3 possible types of additive on the mileage obtained. The experiment assumed that there is an interaction between gasoline type and the type of additive,
hence, a two-factor ANOVA was employed in the data analysis. It was decided to run 36 motors – 4 in each factor level combinations. The following are the analysis results

MEAN

  ADDITIVE 1 ADDITIVE 2 ADDITIVE 3  
GAS TYPE 1 125.825  130.775 128.275 128.2917
GAS TYPE 2 127 133.6 137.825 132.8083
GAS TYPE 3 126.35 132.5 123 127.2833
  126.3917 132.2917 129.7 129.4611

Analysis of Variance Table

  Df Sum Sq Mean Sq F Value Pr(>F)
factor(gas.type) 2 207.7706 103.8853 11.08482 0.000306
factor(additive)  2 209.8872 104.9436 11.19775 0.000287
factor(gas.type):factor(additive)  4 262.9678 65.74194 7.01483 0.000523
Residuals 27 253.04 9.371852 NA NA

a.) Is there a significant interaction between the type of gasoline and the type of additive? Why?
b.) What does the result on the test for significant interaction imply?
c.) Say you are to choose between the three gasoline types, regardless of the type of additive used and considering all other factors constant. Which gasoline would you prefer for your motor and why?

 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Anova and Design of Experiments
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman