REM (rapid eye movement) sleep is sleep during which most dreams occur. Each nig
ID: 3160542 • Letter: R
Question
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 normally distributed for both children and adults. A random sample of n1 = 10 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that 1 = 0.6 hour. Another random sample of n2 = 10 adults showed that they had an average REM sleep time of x2 = 1.70 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?What is the value of the sample test statistic? (Test the difference 12. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four 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 adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 10 children (9 years old) showed that they had an average REM sleep time of x1 = 2.5 hours per night. From previous studies, it is known that 1 = 0.6 hour. Another random sample of n2 = 10 adults showed that they had an average REM sleep time of x2 = 1.70 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?
What is the value of the sample test statistic? (Test the difference 12. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(a) What is the level of significance?
What is the value of the sample test statistic? (Test the difference 12. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Explanation / Answer
a)
As given,
level of significance = 0.01 [ANSWER]
*********************************
b)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 <= 0
Ha: u1 - u2 > 0
At level of significance = 0.01
As we can see, this is a right tailed test.
Calculating the means of each group,
X1 = 2.5
X2 = 1.7
Calculating the standard deviations of each group,
s1 = 0.6
s2 = 0.8
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 10
n2 = sample size of group 2 = 10
Also, sD = 0.316227766
Thus, the z statistic will be
z = [X1 - X2 - uD]/sD = 2.529822128 [ANSWER, TEST STATISTIC]
****************************************
c)
where uD = hypothesized difference = 0
Hence, the P value is, as this is right tailed,
p = 0.010482426 [ANSWER, P VALUE]
*************************************
As P > 0.01, we fail to reject Ho. There is no significant evidence at 0.01 level that children tend to have more REM sleep than adults. [CONCLUSION]
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.