3. + Question Details My Notes Ask Your Teacher REM (rapid eye movement) sleep i

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3. + Question Details 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 adultst. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 children (9 years old) showed that they had an average REM sleep time of x1-2.8 hours per night. From previous studies, it is known that ?? = 0.7 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of X2 = 1.90 hours per night. Previous studies show that ?2-0.8 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. (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with 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 population distributions are approximately normal with unknown standard deviations. 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 ?1-12. Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Explanation / Answer

The statistical software output for this problem is:

Two sample Z summary hypothesis test:
?1 : Mean of population 1 (Std. dev. = 0.7)
?2 : Mean of population 2 (Std. dev. = 0.8)
?1 - ?2 : Difference between two means
H0 : ?1 - ?2 = 0
HA : ?1 - ?2 > 0

Hypothesis test results:

Hence,

a) Level of significance = 0.01

Hypotheses: Option B is correct.

b) Option D is correct.

Test statistic = 2.54

c) P - Value = 0.0055

Graph B is correct.

d) Option C is correct.

e) Option B is correct.

Difference n1 n2 Sample mean Std. err. Z-stat P-value ?1 - ?2 9 9 0.9 0.35433819 2.5399463 0.0055

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