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, = 10 children (9 years old) showed that they had an average REM sleep time of x, = 2.6 hours per night. From previous studies, it is known that o, = 0.5 hour. Another random sample of n, = 10 adults showed that they had an average REM sleep time of x, = 1.80 hours per night. Previous studies show that o, = 0.9 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 P Ho: H1 = Hzi HqiH1>Hz O Ho: H1 = H2i Hii Hy # Hz O Ho: H1< Hzi Hgi Mq = H2 O Ho: H1 = Hzi Hii Mq< Hz %3D (b) What sampling distribution will you use? What assumptions are you making? OP The standard normal. 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 known 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 u, - Hy. Round your answer to two decimal places.)
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, = 10 children (9 years old) showed that they had an average REM sleep time of x, = 2.6 hours per night. From previous studies, it is known that o, = 0.5 hour. Another random sample of n, = 10 adults showed that they had an average REM sleep time of x, = 1.80 hours per night. Previous studies show that o, = 0.9 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 P Ho: H1 = Hzi HqiH1>Hz O Ho: H1 = H2i Hii Hy # Hz O Ho: H1< Hzi Hgi Mq = H2 O Ho: H1 = Hzi Hii Mq< Hz %3D (b) What sampling distribution will you use? What assumptions are you making? OP The standard normal. 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 known 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 u, - Hy. Round your answer to two decimal places.)
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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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, = 10 children (9 years old) showed that they had an
average REM sleep time of x, = 2.6 hours per night. From previous studies, it is known that o, = 0.5 hour. Another random sample of n, = 10 adults showed that they had an average
REM sleep time of x, = 1.80 hours per night. Previous studies show that o, = 0.9 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 P Ho: H1 = Hz; Hqi H1>Hz
O Ho: H1 = H2i H;: H1 # H2
O Ho: H1< Hzi H;: H1 = H2
O Ho: H1 = H2i H;: H1< Mz
(b) What sampling distribution will you use? What assumptions are you making?
OP The standard normal. 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 known 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 u,
Hz. Round your answer to two decimal places.)
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