One way to measure the amount of sleep "activeness" is to measure the percentage of total sleep that is made up of Rapid Eye Movement (REM) sleep. 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 sleeper to sleeper. In an experimental study, sleep researchers examine 8 adults who are classified as "very active" in their daily lives (according to such criteria as amount of exercise and type of occupation), 8 who are classified as "moderately active," and 8 who are classified as "inactive." The researchers record, for each participant, the percentage of total sleep time over the course of four nights that is spent in REM sleep. The summary is as follows: Group Sample Sample Sample size mean variance Very active 8 26.1 12.0 Moderately active 8 21.4 11.9 Inactive 8 24.2 2.9 Send data to calculator v Send data to Excel Assume that the populations of REM sleep percentages from which the samples were drawn are approximately normally distributed and have the same mean and the same variance. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. (a) Give an estimate of this common population variance by pooling the sample variances given. (b) Give an estimate of this common population variance based on the variance of the sample means given