12. [-/4.08 Points] DETAILS BBUNDERSTAT 12 8 5.015. MY NOTES ASK YOUR TEACHER 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 nor distributed for both children and adults. A random sample of 0, = 11 children (9 years old) showed that they had an average REM sleep time of x, = 2.9 hours per night. From previous studies, it is known that , = 0.6 hour. Another random sample of , = 11 adults showed that they had an average REM sleep time of x2 = 2.20 hours per night. Previous studies show that s, = 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. (a) What is the level of significance? State the null and alternate hypotheses O Hom P2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are app h known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both oximately normal with unknown standard deviations