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 ofn
₁ = 9 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 ?₁ = 0.7 hour. Another random sample ofn
₂ = 9 adults showed that they had an average REM sleep time of x₂ = 2.20 hours per night. Previous studies show that ?₂ = 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-Sketch the sampling distribution and show the area corresponding to theP-value.