12. Comparing ANOVA and the t test for an independent-measures hypothesis test Suzanne Zeedyk, a developmental psychologist at Dundee University's School of Psychology, conducted a pilot study in which parents started a half- hour walk with their infants in a parent-facing or an away-facing stroller and then switched to the other type of stroller midway. Her results suggest that parents talked less to the babies, the babies had higher heart rates, and they were less likely to fall asleep in away-facing strollers than in parent- facing strollers. You are interested in testing the hypothesis that babies who travel in parent-facing strollers have different expressive vocabularies than babies who travel in away-facing strollers. You randomly assign 18 newboms to parent-facing strollers and 18 newborns to away-facing strollers. You then test the babies expressive vocabularies at age 36 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's expressive vocabulary. The sample means and sums of squares of the scores for each of the groups are presented in the following table. Group Away-facing Parent-facing Sample Mean Sum of Squares 2,828.97 2,530.28 92.7 Within Treatments Total 104.3 You decide to use an ANOVA at o-0.05 to test the null hypothesis that there is no difference between the groups. The ANOVA table follows. Calculate the F-ratio and enter it into the table. Source of Variation Sum of Squares Between Treatments 1,211.04 5,359.25 6,570.29 ANOVA Table Degrees of Freedom 34 35 Mean Square 1.211.04 157.63 F W Use the Distributions tool that follows to find Fritical at a significance level of 0.05, the value of F that bounds the critical region for the F-ratio test statistic

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
Need help right away
12. Comparing ANOVA and the t test for an independent-measures hypothesis test
Suzanne Zeedyk, a developmental psychologist at Dundee University's School of Psychology, conducted a pilot study in which parents started a half-
hour walk with their infants in a parent-facing or an away-facing stroller and then switched to the other type of stroller midway. Her results suggest
that parents talked less to the babies, the babies had higher heart rates, and they were less likely to fall asleep in away-facing strollers than in parent-
facing strollers.
You are interested in testing the hypothesis that babies who travel in parent-facing strollers have different expressive vocabularies than babies who
travel in away-facing strollers. You randomly assign 18 newboms to parent-facing strollers and 18 newborns to away-facing strollers. You then test the
babies expressive vocabularies at age 36 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's
expressive vocabulary.
The sample means and sums of squares of the scores for each of the groups are presented in the following table.
Group
Away-facing
Parent-facing
Sample Mean Sum of Squares
,828.97
2,530.28
92.7
Source of Variation
Between Treatments
Within Treatments
Total
104.3
You decide to use an ANOVA at o-0.05 to test the null hypothesis that there is no difference between the groups. The ANOVA table follows. Calculate
the F-ratio and enter it into the table.
Sum of Squares
1,211.04
5,359.25
6,570.29
ANOVA Table
Degrees of Freedom
34
35
Mean Square
1.211.04
157.63
F
I'M
Use the Distributions tool that follows to find Fritical at a significance level of 0.05, the value of F that bounds the critical region for the F-ratio test
statistic.
Transcribed Image Text:12. Comparing ANOVA and the t test for an independent-measures hypothesis test Suzanne Zeedyk, a developmental psychologist at Dundee University's School of Psychology, conducted a pilot study in which parents started a half- hour walk with their infants in a parent-facing or an away-facing stroller and then switched to the other type of stroller midway. Her results suggest that parents talked less to the babies, the babies had higher heart rates, and they were less likely to fall asleep in away-facing strollers than in parent- facing strollers. You are interested in testing the hypothesis that babies who travel in parent-facing strollers have different expressive vocabularies than babies who travel in away-facing strollers. You randomly assign 18 newboms to parent-facing strollers and 18 newborns to away-facing strollers. You then test the babies expressive vocabularies at age 36 months using the Expressive Vocabulary Test (EVT), which is designed primarily to assess children's expressive vocabulary. The sample means and sums of squares of the scores for each of the groups are presented in the following table. Group Away-facing Parent-facing Sample Mean Sum of Squares ,828.97 2,530.28 92.7 Source of Variation Between Treatments Within Treatments Total 104.3 You decide to use an ANOVA at o-0.05 to test the null hypothesis that there is no difference between the groups. The ANOVA table follows. Calculate the F-ratio and enter it into the table. Sum of Squares 1,211.04 5,359.25 6,570.29 ANOVA Table Degrees of Freedom 34 35 Mean Square 1.211.04 157.63 F I'M Use the Distributions tool that follows to find Fritical at a significance level of 0.05, the value of F that bounds the critical region for the F-ratio test statistic.
Now evaluate the null hypothesis that the population means for all treatments are equal. At a significance level of a 0.05, the null hypothesis is
You find that you
conclude that the direction that the stroller faces influences a child's expressive vocabulary at 36
months.
Now you decide to use a t test to test the hypothesis that there is no difference between the groups. The estimated standard error (SM-M) is 4.19,
so the t test statistic is
Use the following tool to find the critical regions for a = 0.05.
t Distribution
Degrees of Freedom = 21
-3.0
-2.0
2500
-1.0
5000
5000
15000
laskiol
0.0
-0.686 0.000 0.686
1.0
2.0
3.0
Now use the tool to evaluate the null hypothesis. At a significance level of a = 0.05, the null hypothesis is
conclude that the direction the stroller faces influences a child's expressive vocabulary at 36 months.
t
The critical t-scores (the values for t-scores that separate the tails from the main body of the distribution, forming the critical regions) are
.You find that you
When you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and the t test resulted in
conclusion.
Transcribed Image Text:Now evaluate the null hypothesis that the population means for all treatments are equal. At a significance level of a 0.05, the null hypothesis is You find that you conclude that the direction that the stroller faces influences a child's expressive vocabulary at 36 months. Now you decide to use a t test to test the hypothesis that there is no difference between the groups. The estimated standard error (SM-M) is 4.19, so the t test statistic is Use the following tool to find the critical regions for a = 0.05. t Distribution Degrees of Freedom = 21 -3.0 -2.0 2500 -1.0 5000 5000 15000 laskiol 0.0 -0.686 0.000 0.686 1.0 2.0 3.0 Now use the tool to evaluate the null hypothesis. At a significance level of a = 0.05, the null hypothesis is conclude that the direction the stroller faces influences a child's expressive vocabulary at 36 months. t The critical t-scores (the values for t-scores that separate the tails from the main body of the distribution, forming the critical regions) are .You find that you When you evaluated the mean difference from the independent-measures study comparing only two samples, the ANOVA and the t test resulted in conclusion.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 1 images

Blurred answer
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