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 variation	Degrees of freedom	Sum of squares	Mean square	Fstatistic
Treatments (between groups)	2	38.83	19.42	3.37
Error (within groups)	18	103.80	5.77
Total	20	142.63

(b)How many groups of adults were studied in the experiment?

(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?

0.01

(d)What is thep-value corresponding to theFstatistic for the ANOVA test? Round your answer to at least three decimal places.

0.99

(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