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 adultst. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 8 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 ơ, = 0.6 hour. Another random sample of n, = 8 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that o, = 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 Hoi H1 = Hz; HHy> H2 O Hoi Hy

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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 adultst. Assume that REM sleep time is normally distributed for both children and adults. A
random sample of n, = 8 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 o, = 0.6 hour. Another random sample of n, = 8 adults showed that they had an average REM sleep time of
x2 = 2.10 hours per night. Previous studies show that o, = 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 Ho: H1 = H2i HiitHy> H2
O Ho: H,<Hz; H;:Hy = H2
O Ho: H1 = H2; H:H, * H2
O Ho: H1 = H2; H;:Hy<Hz
(b) What sampling distribution will you use? What assumptions are you making?
O The Student's t. We assume that both population distributions are approximately normal with unknown 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 known standard deviations.
O The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
What is the value of the sample test statistic? (Test the difference u, - Hz. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Transcribed Image Text: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 adultst. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n, = 8 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 o, = 0.6 hour. Another random sample of n, = 8 adults showed that they had an average REM sleep time of x2 = 2.10 hours per night. Previous studies show that o, = 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 Ho: H1 = H2i HiitHy> H2 O Ho: H,<Hz; H;:Hy = H2 O Ho: H1 = H2; H:H, * H2 O Ho: H1 = H2; H;:Hy<Hz (b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with unknown 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 known standard deviations. O The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Test the difference u, - Hz. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
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