M(rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. wever, it is thought that children have more REM sleep than adultst. Assume that REM sleep time is normally distributed for both dren and adults. A random sample of n, = 9 children (9 years old) showed that they had an average REM sleep time of x, = 2. urs per night. From previous studies, it is known that o, = 0.7 hour. Another random sample of n, = 9 adults showed that they %3! an average REM sleep time of x, 2.00 hours per night. Previous studies show that o, = 0.9 hour. Do these data indicate that 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? O 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 Student'st. 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 standa deviations. What is the value of the sample test statistic? (Test the difference u, - ,, 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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15)
Sketch the sampling distribution and show the area corresponding to the P-value.
Th
Z:
o-3
-2
1
-3
-2
-1
1
Si
P-
(F
o-3
-2
-1
3
o-3
-2
-1
13
S-
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant
at level a?
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
Coc
This
(e) Interpret your conclusion in the context of the application.
O Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for
adults
mark
use
mor
O Reject the null hypothesis, there is insufficient evidence that the mean REM seep time for children is more than for adults.
O Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for ch ldren is more than for adults.
O Fail to reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults.
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Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. Th Z: o-3 -2 1 -3 -2 -1 1 Si P- (F o-3 -2 -1 3 o-3 -2 -1 13 S- (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. Coc This (e) Interpret your conclusion in the context of the application. O Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults mark use mor O Reject the null hypothesis, there is insufficient evidence that the mean REM seep time for children is more than for adults. O Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for ch ldren is more than for adults. O Fail to reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults. Need Help? Read It EWatch It
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, = 9 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, = 0.7 hour. Another random sample of n,
= 9 adults showed that they
had an average REM sleep time of x, = 2.00 hours per night. Previous studies show that a, = 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.
(b) What sampling distribution will you use? What assumptions are you making?
O 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 Student'st. 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.
What is the value of the sample test statistic? (Test the difference u, -H,, 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, = 9 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, = 0.7 hour. Another random sample of n, = 9 adults showed that they had an average REM sleep time of x, = 2.00 hours per night. Previous studies show that a, = 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. (b) What sampling distribution will you use? What assumptions are you making? O 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 Student'st. 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. What is the value of the sample test statistic? (Test the difference u, -H,, 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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