REM (rapid eye movement) sleep is sleep during which most dreams ocour. Each night a person has both REM and non-REM sdeep. However, tis thought that children have more REM sleep than adultst. Assume that REM sleep time is normally distributed for both children and aduts. A random sample of a,- 1i children (9 years old) showed that they had an average REM sleep time of, -2.5 hours per night From previous studies, is known hat, -0.6 hour. Another random sample of n- 11 aduts shawed that they had an average REM sieep time of- 1.90 hours per night. Previous studies show that ,-0.5 hour. De these data indicate that, an average, hildren tend to have more REM sleep than adults use a 1% level or significance. al what is the level of significance State the nul and alternate hypotheses OM (B) What sampling distribution wi you use? what assumptions are yau making? The standard normal. We assume that bath population distributions are approximately normal with known standard devilations. O The StudentSE We assume that both population distributions are approximately normal with unknown standard deviations. O The standard normal. We assume that bath papulation distributions are appraximately normal with unknown standard deviations O The StudertsE We assume that both population distributions are approximataly normal with known standard deviations. What is the value of the sample test statistic? (TesE the diference , - Round your answer to two decimal places. O Find for estimate) the Pvalue. (Round your anower to four dedimal places.) Sketch the sampling distribution and show the area comesponding to the Pvalue. -3 -1 2 (4) Based on your answers in parts (a) to (), wil you reject or fal to reject the nul hypothesis? Are the data statisticaly significant a level a OAt the e0.01 level, we fail to reject the ul hypothesis and candude the data are statistically significart. O At the e-0.0s level, we reject the null hypothesis and conclude the data are nat statistically signifcant. O At the e-0.0s level, we fail to reject the nul hypothesis and candude the data are not statistically significant. O At the e-0.0s level, we reject the null hypothesis and conclude the data are statistically significant (4) Interpret your condusion in the context of the application. O Fail to reject the null hypothesis, there is insuficient evidence that the mean REM sleep time for children is mare than for adults O Reject the nul hypothesis, there s insumcient evidonce that the mean REM sleep time for chidren is more than for adults O Fail to reject the null hypothesis, there is suficient evidence that the mean REM sleep time for children is more than for adults. O Reject the nul hypothesis, there is sufdent evidence that the mean REM sieep time for children is more than for aduts.