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 = 8 children (9 years old) showed that they had an average REM sleep time of x1 = 2.6 hours per night. From previous studies, it is known that σ1 = 0.6 hour. Another random sample of n2 = 8 adults showed that they had an average REM sleep time of x2 = 1.90 hours per night. Previous studies show that σ2 = 0.5 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Name: REM (rapid eye movement) sleep is sleep during which most dreams occur
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Description: 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

The test statistic is obtained as below: z=x1¯-x2¯-μ1-μ2σ12n1+σ22n2 Here, n1=8x1¯=2.6σ1=0.6n2=8x2¯=1.90σ2=0.5μ1-μ2=0The test statistic for testing μ1-μ2=0 is, z=2.6-1.90-00.628+0.528=0.70.368+0.258=0.70.0450+0.0313=0.70.2761=3.1506 Thus, the test statistic value is 3.1506p- value: The P-value is obtained Excel function “=NORMSDIST(z)”. Output obtained from Excel is given below: From the output, the P-value is 0.0008(=(1-0.9992)Answer: Thus, the value of sample test statistic is 3.1506 Thus, the p-value is 0.0008

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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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 = 8 children (9 years old) showed that they had an average REM sleep time of x₁ = 2.6 hours per night. From previous studies, it is known that σ₁ = 0.6 hour. Another random sample of n₂ = 8 adults showed that they had an average REM sleep time of x₂ = 1.90 hours per night. Previous studies show that σ₂ = 0.5 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance.

What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to two decimal places.)

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

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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