Rapid Eye Movement (REM) sleep, often linked with dreaming, is marked by very high brain activity. In fact, REM periods may be the sleep periods in which the brain is most active. REM sleep takes up a mean of about 25% of the total sleep time, but this varies from person to person. Suppose that in an experimental study, sleep researchers examine 10 adults who are classified as "very active" in their daily lives, 10 who are classified as "moderately active," and 10 who are classified as "inactive." The researchers record, for each participant, the percentage of total sleep time over the course of several nights that is spent in REM sleep. The summary is as follows. Groups Very active Moderately active Inactive Send data to Excel Sample Sample size mean 10 Between groups Error (within groups) Total 10 10 Yes 25.2 Source of Degrees of Sum of variation freedom squares 0 36.47 23.8 The researchers do a one-way, independent-samples ANOVA test of the hypothesis that there is no difference in percentage of sleep time spent in REM among the three populations of "very active," "moderately active," and "inactive" adults. No 26.5 (a) This ANOVA test is summarized in the (partially filled) ANOVA table below. Fill in the remaining cells of this ANOVA table. (In the ANOVA table, round your answers for the mean squares and the F statistic to at least two decimal places each.) 0 0 Sample variance 8.6 183.60 3.2 220.07 8.6 Mean square F statistic (b) Using the 0.05 level of significance, what is the critical value of the F statistic for the ANOVA test? Round your answer to at least two decimal places. X (c) Can the researchers conclude, using the 0.05 level of significance, that at least one of the populations of adults differs from the others in mean percentage of sleep time spent in REM? 5
Rapid Eye Movement (REM) sleep, often linked with dreaming, is marked by very high brain activity. In fact, REM periods may be the sleep periods in which the brain is most active. REM sleep takes up a mean of about 25% of the total sleep time, but this varies from person to person. Suppose that in an experimental study, sleep researchers examine 10 adults who are classified as "very active" in their daily lives, 10 who are classified as "moderately active," and 10 who are classified as "inactive." The researchers record, for each participant, the percentage of total sleep time over the course of several nights that is spent in REM sleep. The summary is as follows. Groups Very active Moderately active Inactive Send data to Excel Sample Sample size mean 10 Between groups Error (within groups) Total 10 10 Yes 25.2 Source of Degrees of Sum of variation freedom squares 0 36.47 23.8 The researchers do a one-way, independent-samples ANOVA test of the hypothesis that there is no difference in percentage of sleep time spent in REM among the three populations of "very active," "moderately active," and "inactive" adults. No 26.5 (a) This ANOVA test is summarized in the (partially filled) ANOVA table below. Fill in the remaining cells of this ANOVA table. (In the ANOVA table, round your answers for the mean squares and the F statistic to at least two decimal places each.) 0 0 Sample variance 8.6 183.60 3.2 220.07 8.6 Mean square F statistic (b) Using the 0.05 level of significance, what is the critical value of the F statistic for the ANOVA test? Round your answer to at least two decimal places. X (c) Can the researchers conclude, using the 0.05 level of significance, that at least one of the populations of adults differs from the others in mean percentage of sleep time spent in REM? 5
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Rapid Eye Movement (REM) sleep, often linked with dreaming, is marked by very high brain activity. In fact, REM periods
may be the sleep periods in which the brain is most active. REM sleep takes up a mean of about 25% of the total sleep time,
but this varies from person to person.
Suppose that in an experimental study, sleep researchers examine 10 adults who are classified as "very active" in their daily
lives, 10 who are classified as "moderately active," and 10 who are classified as "inactive." The researchers record, for each
participant, the percentage of total sleep time over the course of several nights that is spent in REM sleep. The summary is
as follows.
Groups
Very active
Moderately
active
Inactive
Send data to Excel
Sample Sample
size
mean
10
Between
groups
Error
(within
groups)
Total
10
10
Yes
25.2
Source of Degrees of Sum of
variation freedom squares
23.8
The researchers do a one-way, independent-samples ANOVA test of the hypothesis that there is no difference in percentage
of sleep time spent in REM among the three populations of "very active," "moderately active," and "inactive" adults.
No
26.5
(a) This ANOVA test is summarized in the (partially filled) ANOVA table below. Fill in the remaining cells of this ANOVA
table. (In the ANOVA table, round your answers for the mean squares and the F statistic to at least two decimal
places each.)
1
0
36.47
Sample
variance
8.6
183.60
220.07
3.2
8.6
X
Mean
square
F statistic
(b) Using the 0.05 level of significance, what is the critical value of the F statistic for the ANOVA test? Round your answer
to at least two decimal places.
U
0
X
(c) Can the researchers conclude, using the 0.05 level of significance, that at least one of the populations of adults
differs from the others in mean percentage of sleep time spent in REM?
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