REM (racid eye movement) sleep is sleep durtng whach most dreams ocur. tach ght a person has both REM and non REM eep. However, it theught that chren have more REM dep than ad . A e that ep tmeomaly detred r bth chdren and a A random sample of n, 11 children (9 years old) showed that they had an average REM sleep time of x,29 hours per night. Prem prevtous stade, tis knewn that hours per nght. Prevtous studies show that o,0.9 hour. De these data indicate that, on average, chedren tend to have more REM seep than adus uea 1s level of sigance Nour. Anether random sample of,11 ad.s shewed that they had a e REM ep tae of.-8 (a) what is the level of gncance? State the null and altemate hypotheses OH H-M H (b) what sampeng dstribution will you une? what assumptions are you making? O The Student's t. We assume that both population dintributions are approimately normal with known standard devatons O The Student's t. We assume that both population diatributions are approxmately normal with unknown standard deviations O The standard normal. We assume that both populaton distributiens are appreximately nermal with unknown standard devtabens O The standard normal. we assume that both population distributions are appreximately nermal with known standard devtatons what is the value of the sample test statisbc (Test the dference , - Round your answer to two decmal places.) () Find (or estimate) the Pvalue. (Round your ansner to four decmal places.) Sketch the sampling distribution and show the area comresponding to the Pvalue

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REM (rapid eye movement) sleep is sleep during which most dreams ocur. Each night a person has both REM and non-REM sleep. However, it is theught that chdren have more REM sleep than adtst. Assume that REM seep tme is normally distrib.ted for both chdren and ad.A
random sample of n,11children (9 years old) showed that they had an average REM sleep time of x,2.9 hours per night. From prevtous studies, tis known that o,0.5 hour. Another random sample ofn,-11 aduts showed that they had an average REH enp tame of ,2.10
hours per night. Previous studies show that a, = 0.9 hour. Do these data indicate that, on average, chdren tend to have more REM sleep than adults? Use a 1% level of signafcance.
a) what is the level of significance?
state the null and alternate hypotheses.
O H 4, - Hai H, >
(b) what sampling distribution will you use? what assumptions are you making?
O The Student's t. We assume that both population dinstributions 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.
O The standard normal, we assume that both population distributions are appreximately normal with unknown standard devtations.
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,- u Round your answer to two decimal places.)
(c) Find (or estimate) the P.value. (Round your answer to four decmal places.)
Sketch the sampling distribution and show the area coresponding to the Pvalue.
O-3
us 0v 0 4:05
hp
->
esc
backspace
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%24
@
8
3
4
2
y
r
W
Transcribed Image Text:REM (rapid eye movement) sleep is sleep during which most dreams ocur. Each night a person has both REM and non-REM sleep. However, it is theught that chdren have more REM sleep than adtst. Assume that REM seep tme is normally distrib.ted for both chdren and ad.A random sample of n,11children (9 years old) showed that they had an average REM sleep time of x,2.9 hours per night. From prevtous studies, tis known that o,0.5 hour. Another random sample ofn,-11 aduts showed that they had an average REH enp tame of ,2.10 hours per night. Previous studies show that a, = 0.9 hour. Do these data indicate that, on average, chdren tend to have more REM sleep than adults? Use a 1% level of signafcance. a) what is the level of significance? state the null and alternate hypotheses. O H 4, - Hai H, > (b) what sampling distribution will you use? what assumptions are you making? O The Student's t. We assume that both population dinstributions 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. O The standard normal, we assume that both population distributions are appreximately normal with unknown standard devtations. 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,- u Round your answer to two decimal places.) (c) Find (or estimate) the P.value. (Round your answer to four decmal places.) Sketch the sampling distribution and show the area coresponding to the Pvalue. O-3 us 0v 0 4:05 hp -> esc backspace & %24 @ 8 3 4 2 y r W
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