Do both short problems 5REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has bothREM and non-REM sleep. However, it is thought that children have more REM sleep than adultst. Assumethat REM sleep time is normally distributed for both children and adults. A random sampleof m= 11 children (9 years old) showed that they had an average REM sleep time of x₁ = 2.9 hours pernight. From previous studies, it is known that o₁ = 0.6 hour. Another random sample of m2 = 11 adultsshowed that they had an average REM sleep time of x2 = 2.50 hours per night. Previous studies show that0 2 = 0.5 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults?Use a 10% level of significance. Solve the problem using both the traditional method and the P-valuemethod. (Test the difference μ1-2. Round the test statistic and critical value to two decimal places.Round the P-value to four decimal places.)test statisticcritical valueP-valueConclusionFail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for childrenis more than for adults. Reject the null hypothesis, there is insufficient evidence that the mean REMsleep time for children is more than for adults. Fail to reject the null hypothesis, there is sufficient1evidence that the mean REM sleep time for children is more than for adults. Reject the null hypothesis,there is sufficient evidence that the mean REM sleep time for children is more than for adults.Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?These two methods differ slightly. The conclusions obtained by using both methods are the same.OWe reject the null hypothesis using the traditional method, but fail to reject using the P-value method.We reject the null hypothesis using the P-value method, but fail to reject using the traditional method. 4A random sample of m= 10 regions in New England gave the following violent crime rates (per millionpopulation).X₁: New England Crime Rate3.3 3.9 4.2 4.1 3.3 4.1 1.8 4.8 2.9 3.1Another random sample of m2 = 12 regions in the Rocky Mountain states gave the following violent crimerates (per million population).X2: Rocky Mountain Crime Rate3.5 4.1 4.7 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8USE SALTAssume that the crime rate distribution is approximately normal in both regions. Do the data indicate thatthe violent crime rate in the Rocky Mountain region is higher than in New England? Use x = 0.01. Solvethe problem using both the traditional method and the P-value method. (Test the difference μ 1 - μ2.Round the test statistic and critical value to three decimal places.)test statisticcritical valueFind (or estimate) the P-value.P-value > 0.250 0.125 < P-value < 0.2500.005< P-value < 0.025 P-value < 0.0050.050 < P-value < 0.125 0.025 < P-value < 0.050ConclusionFail to reject the null hypothesis, there is sufficient evidence that violent crime in the Rocky Mountainregion is higher than in New England. Reject the null hypothesis, there is sufficient evidence thatviolent crime in the Rocky Mountain region is higher than in New England. Fail to reject the nullhypothesis, there is insufficient evidence that violent crime in the Rocky Mountain region is higher than inNew England. Reject the null hypothesis, there is insufficient evidence that violent crime in the RockyMountain region is higher than in New England.Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?The conclusions obtained by using both methods are the same. We reject the null hypothesis usingthe traditional method, but fail to reject using the P-value method. These two methods differ slightly.We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.

As per the Bartleby guildlines we have solve first question and rest can be reposted.... We have to…

5 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 = 11 children (9 years old) showed that they had an average REM sleep time of x₁ = 2.9 hours per night. From previous studies, it is known that o₁ = 0.6 hour. Another random sample of n₂ = 11 adults showed that they had an average REM sleep time of x2 = 2.50 hours per night. Previous studies show that 0 ₂ = 0.5 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 10% level of significance. Solve the problem using both the traditional method and the P-value method. (Test the difference μ1-2. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.) test statistic critical value P-value Conclusion Fail to reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults. Reject the null hypothesis, there is insufficient evidence that the mean REM sleep time for children is more than for adults. Fail to reject the null hypothesis, there is sufficient

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P