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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 several groups of adults who are drawn from different populations (one group from each population). These populations differ in amount of typical daily activity (ranging from "very active" to "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 researchers then perform a one-way, independent-samples ANOVA test of the equality of the mean REM sleep percentages of the different populations. (a) Here is a summary of their ANOVA test. Fill in the missing entry of the table (rounded to two decimal places). Source of Degrees of Sum of Mean square F statistic X G B ? variation freedom squares Between 5 98.98 19.80 groups Error (within groups) 36 354.00 9.83 Total 41 452.98 0 (b) How many groups of adults were studied in the experiment? x 5 (c) For the ANOVA test, it is assumed that the variances of REM sleep time percentages are the same for each population of adults. What is an unbiased estimate of this common population variance based on the sample variances? 10 X 5 (d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places. X G (e) 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? Yes No 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 several groups of adults who are drawn from different populations (one group from each population). These populations differ in amount of typical daily activity (ranging from "very active" to "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 researchers then perform a one-way, independent-samples ANOVA test of the equality of the mean REM sleep percentages of the different populations. (a) Here is a summary of their ANOVA test. Fill in the missing entry of the table (rounded to two decimal places). Source of Degrees of Sum of Mean square F statistic X G B ? variation freedom squares Between 5 98.98 19.80 groups Error (within groups) 36 354.00 9.83 Total 41 452.98 0 (b) How many groups of adults were studied in the experiment? x 5 (c) For the ANOVA test, it is assumed that the variances of REM sleep time percentages are the same for each population of adults. What is an unbiased estimate of this common population variance based on the sample variances? 10 X 5 (d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places. X G (e) 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? Yes No 5

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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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 several groups of adults who are drawn from different populations (one group from each population). These populations differ in amount of typical daily activity (ranging from "very active" to "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 researchers then perform a one-way, independent-samples ANOVA test of the equality of the mean REM sleep percentages of the different populations. (a) Here is a summary of their ANOVA test. Fill in the missing entry of the table (rounded to two decimal places). Source of Degrees of Sum of Mean square F statistic X G B ? variation freedom squares Between 5 98.98 19.80 groups Error (within groups) 36 354.00 9.83 Total 41 452.98 0 (b) How many groups of adults were studied in the experiment? x 5 (c) For the ANOVA test, it is assumed that the variances of REM sleep time percentages are the same for each population of adults. What is an unbiased estimate of this common population variance based on the sample variances? 10 X 5 (d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places. X G (e) 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? Yes No 5
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 several groups of adults who are drawn from different populations (one group from each population). These populations differ in amount of typical daily activity (ranging from "very active" to "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 researchers then perform a one-way, independent-samples ANOVA test of the equality of the mean REM sleep percentages of the different populations. (a) Here is a summary of their ANOVA test. Fill in the missing entry of the table (rounded to two decimal places). Source of Degrees of Sum of Mean square F statistic X G B ? variation freedom squares Between 5 98.98 19.80 groups Error (within groups) 36 354.00 9.83 Total 41 452.98 0 (b) How many groups of adults were studied in the experiment? x 5 (c) For the ANOVA test, it is assumed that the variances of REM sleep time percentages are the same for each population of adults. What is an unbiased estimate of this common population variance based on the sample variances? 10 X 5 (d) What is the p-value corresponding to the F statistic for the ANOVA test? Round your answer to at least three decimal places. X G (e) 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? Yes No 5
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