4. A two-factor ANOVA: the null hypotheses, interpretation, and assumptions A fourth-grade teacher suspects that the time she administers a test, and what sort of snack her students have before the test, affects their performance. To test her theory, she assigns 90 fourth-grade students to one of three groups. One group gets candy (a lollipop) for their 9:55 AM snack. Another group gets a high-protein snack (beef jerky) for their 9:55 AM snack. The third group does not get a 9:55 AM snack. The teacher also randomly assigns 10 of the students in each snack group to take the test at three different times: 10:00 AM (right after snack), 11:00 AM (an hour after snack), and 12:00 PM (right before lunch). Suppose that the teacher uses a two-factor independent-measures ANOVA to analyze these data. Without post hoc tests, which of the following questions can be answered by this analysis? (Note: Assume that receiving no snack is considered one type of snack.) Check all that apply. Is there a difference among the scores for the snack types because students who have no snack are hungry? Does student performance on the test depend on the time of the test? Do students who are tested at 11:00 AM score higher than students who are tested at 12:00 PM? Does the type of snack (or lack of snack) affect student performance on the test? In the following table are the mean test scores for each of these nine different combinations of snack type and test timing. Factor A: Type of Snack Factor B: Time of Test 10:00 AM Candy Snack Protein Snack No Snack M = 92.0 M = 88.5 M = 90.0 M = 90.2 11:00 AM M = 84.0 M = 88.0 M = 91.0 M = 87.7 12:00 PM M = 88.0 M = 87.5 M = 83.0 M = 86.2 M = 88.0 M = 88.0 M = 88.0
4. A two-factor ANOVA: the null hypotheses, interpretation, and assumptions A fourth-grade teacher suspects that the time she administers a test, and what sort of snack her students have before the test, affects their performance. To test her theory, she assigns 90 fourth-grade students to one of three groups. One group gets candy (a lollipop) for their 9:55 AM snack. Another group gets a high-protein snack (beef jerky) for their 9:55 AM snack. The third group does not get a 9:55 AM snack. The teacher also randomly assigns 10 of the students in each snack group to take the test at three different times: 10:00 AM (right after snack), 11:00 AM (an hour after snack), and 12:00 PM (right before lunch). Suppose that the teacher uses a two-factor independent-measures ANOVA to analyze these data. Without post hoc tests, which of the following questions can be answered by this analysis? (Note: Assume that receiving no snack is considered one type of snack.) Check all that apply. Is there a difference among the scores for the snack types because students who have no snack are hungry? Does student performance on the test depend on the time of the test? Do students who are tested at 11:00 AM score higher than students who are tested at 12:00 PM? Does the type of snack (or lack of snack) affect student performance on the test? In the following table are the mean test scores for each of these nine different combinations of snack type and test timing. Factor A: Type of Snack Factor B: Time of Test 10:00 AM Candy Snack Protein Snack No Snack M = 92.0 M = 88.5 M = 90.0 M = 90.2 11:00 AM M = 84.0 M = 88.0 M = 91.0 M = 87.7 12:00 PM M = 88.0 M = 87.5 M = 83.0 M = 86.2 M = 88.0 M = 88.0 M = 88.0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Need help right away
Transcribed Image Text:4. A two-factor ANOVA: the null hypotheses, interpretation, and assumptions
A fourth-grade teacher suspects that the time she administers a test, and what sort of snack her students have before the test, affects their
performance. To test her theory, she assigns 90 fourth-grade students to one of three groups. One group gets candy (a lollipop) for their 9:55 AM
snack. Another group gets a high-protein snack (beef jerky) for their 9:55 AM snack. The third group does not get a 9:55 AM snack. The teacher also
randomly assigns 10 of the students in each snack group to take the test at three different times: 10:00 AM (right after snack), 11:00 AM (an hour
after snack), and 12:00 PM (right before lunch).
Suppose that the teacher uses a two-factor independent-measures ANOVA to analyze these data. Without post hoc tests, which of the following
questions can be answered by this analysis? (Note: Assume that receiving no snack is considered one type of snack.) Check all that apply.
Is there a difference among the scores for the snack types because students who have no snack are hungry?
Does student performance on the test depend on the time of the test?
Do students who are tested at 11:00 AM score higher than students who are tested at 12:00 PM?
Does the type of snack (or lack of snack) affect student performance on the test?
In the following table are the mean test scores for each of these nine different combinations of snack type and test timing.
Factor A: Type of Snack
Factor B: Time of Test
10:00 AM
M = 92.0
M = 88.5
Candy Snack
Protein Snack
No Snack
M = 90.0
M = 90.2
11:00 AM
M = 84.0
M = 88.0
M = 91.0
M = 87.7
12:00 PM
M = 88.0
M = 87.5
M = 83.0
M = 86.2
M = 88.0
M 88.0
M = 88.0
Transcribed Image Text:The following graph shows the mean test scores for the treatment conditions. Use this graph and the data matrix to answer the following questions.
Mean Test Score
94
92
90
88
86
84
82
ВО
78
10:00 AM
11:00 AM
Time Test Is Administered
12 00 PM
Examining the graph and the table of means, which of the following is a null hypothesis that might be rejected using a two-factor analysis of
variance? Check all that apply.
-candy snack.
protein snack
-no snack
There is no interaction between the type of snack and the time of test
10:00 AM = 11:00 AM = 12:00 PM
10:00 AM # H11:00 AM 12:00 PM
Which of the following statements must the teacher assume in order to believe that the results of her two-factor ANOVA are valid? Check all that
apply.
The populations defined by the nine treatment conditions are normally distributed.
The populations defined by the nine treatment conditions have equal variances regardless of snack type or test time.
The test scores within each of the nine samples (one for each treatment condition) are independent.
The populations defined by the nine treatment conditions have equal means regardless of snack type or test time.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman