statistics math

REM (rapid eye movement) sleep is sleep during which most dreams oocur. Each night a person has both REM and non-REM sleep. However, it is thought the children have more REM sleep than adultst. Assume that REM sleep time is normally distributed For both children and adults. A random sample ofn1 = 9 children {9 years old) showed that they had an average REM sleep time of;1 = 2.6 hours per night. From previous studies, it is known that 61 = [1.9 hour. Another random sample of oz = 9 adults showed that they had an average REM sleep time of E2 = 1.?!) hours per night. Previous studies show that oz = 0.7 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of signicance. (a) What is the level of signicance? E State the null and alternate hypotheses. O H,,_,:,u1 = #2; H1: \"1 > \"2 O .l'il,._,:,u1 = 312; Hi: #1 a: #2 0 Hu= #1 d #2: H1= #1 = #2 O .i-if,.,:,u1 = 312; Hi: #1 i #2 (b) What sampling distribution will you use? What assumptions are you making? 0 The standard normal. We assume that both population distributions are approximately normal with known standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? {Test the difference '"1 1:12. Round your answer to two decimal places.) E (c) Find (or estimate) the P-value. (Round your answer to Four decimal places.) E Sketch the sampling distribution and show the area corresponding to the P-value. n 4-1