REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sle

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REM (rapid eye movement) sleep is sleep during which most dreams
occur. Each night a person has both REM and non-REM sleep. However,
it is thought that children have more REM sleep than adults†.
Assume that REM sleep time is normally distributed for both
children and adults. A random sample
of n1 = 8 children (9 years
old) showed that they had an average REM sleep time
of x1 = 2.9 hours per
night. From previous studies, it is known
that 𝜎1 = 0.9 hour. Another random
sample of n2 = 8 adults
showed that they had an average REM sleep time
of x2 = 2.00 hours per
night. Previous studies show
that 𝜎2 = 0.5 hour. Do these data
indicate that, on average, children tend to have more REM sleep
than adults? Use a 1% level of significance.
(a) What is the level of significance?
(b) What is the value of the sample test statistic? (Test the
difference 𝜇1 − 𝜇2. Round your
answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your
answer to four decimal places.)