REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, Ris thought that children have more REM sleep than adultst. Assume that REM sleep time is normaly distributed for both children and aduts. A random sample of e, 10 children (9 years old) showed that they had an average REM sleep X,-2.6 hours per right. From previous studies, itis known that e,0.5 hour. Another random sample of n,- 10 adults showed that they had an average REM sleep time of , 1.80 hours per night. Previous studies show that e,-0.9 hour. Do these data indicate that, on average, chidren tend to have more REM deep than adults? Use a 1s level of significance. (a) what is the level of signitcance? State the nul and aternate hypotheses What sampling dtrbution will ou use? What assumptions are you making The standard nermal. We assume that both population distributons are aporoximately normal with known standard deviations. The standard nomal. We assume that beth population distributions are approximately normal with unknown standard deviations • The Student's t. We assume that beth papulation dstributions are approximately narmal with known standard deviations. The Student's t. We assume that boh papulation distributions are approximately narmal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference- Round your answer to twa decimal places.) 246 () Fed (or estimate) the Pvalue. (Round your answer to four dedimal places.)