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 = 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 ?1 = 0.6 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.20 hours per night. Previous studies show that ?2 = 0.7 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 < ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 > ?2 H0: ?1 = ?2; H1: ?1 < ?2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to two decimal places.) Find (or estimate) the P-value. (Round your answer to four decimal places.) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. Interpret your conclusion in the context of the application. 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 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. Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults.

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 = 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 ?1 = 0.6 hour. Another random sample of n2 = 11 adults showed that they had an average REM sleep time of x2 = 2.20 hours per night. Previous studies show that ?2 = 0.7 hour. Do these data indicate that, on average, children tend to have more REM sleep than adults? Use a 1% level of significance. State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 < ?2; H1: ?1 = ?2 H0: ?1 = ?2; H1: ?1 > ?2 H0: ?1 = ?2; H1: ?1 < ?2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. What is the value of the sample test statistic? (Test the difference ?1 − ?2. Round your answer to two decimal places.) Find (or estimate) the P-value. (Round your answer to four decimal places.) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?? At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. Interpret your conclusion in the context of the application. 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 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. Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults.

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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

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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State the null and alternate hypotheses.

H₀: ?₁ = ?₂; H₁: ?₁ ≠ ?₂

H₀: ?₁ < ?₂; H₁: ?₁ = ?₂

H₀: ?₁ = ?₂; H₁: ?₁ > ?₂

H₀: ?₁ = ?₂; H₁: ?₁ < ?₂

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

What is the value of the sample test statistic? (Test the difference ?₁ − ?₂. Round your answer to two decimal places.)

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

Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

Interpret your conclusion in the context of the application.

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 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.

Reject the null hypothesis, there is sufficient evidence that the mean REM sleep time for children is more than for adults.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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