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 adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 = 9 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 ?1 = 0.8 hour. Another random sample of n2 = 9 adults showed that they had an average REM sleep time of x2 = 2.40 hours per night. Previous studies show that ?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 ?1 − ?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 ConclusionFail to reject the null hypothesis, there is sufficient evidence 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. 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 insufficient 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?The conclusions obtained by using both methods are the same.These two methods differ slightly. We 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.

We have given that Sample size n1= 9b, n2=9 Sample mean xbar1 =2.9 , xbar2 = 0.5 Standard deviation…

Answered: REM (rapid eye movement) sleep is sleep…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 adults†. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n₁ = 9 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 ?₁ = 0.8 hour. Another random sample of n₂ = 9 adults showed that they had an average REM sleep time of x₂ = 2.40 hours per night. Previous studies show that ?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 ?₁ − ?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 sufficient evidence 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. 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 insufficient 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?

The conclusions obtained by using both methods are the same.These two methods differ slightly. We 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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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