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†....

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
n
₁
= 10 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
= 0.6 hour. Another random sample of
n
₂
= 10 adults showed that they had an average REM sleep time of x₂
= 2.20 hours per night. Previous studies show that σ₂
= 0.7 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance.