On average, adults spend approximately 5 hours per night in NREM (non-rapid eye movement) sleep. A sleep study selects a random sample of adults and gives them each a weighted blanket. They would like to know if using the weighted blanket changes the mean number of hours per night of NREM sleep. We want to test = 5 versus ≠ 5 where = the true mean hours of NREM sleep per night for adults who use a weighted blanket.A 99% confidence interval for the true mean hours of NREM sleep per night for adults who use a weighted blanket is (5.1, 5.8) hours.Based on the confidence interval, what conclusion would you make for a test of these hypotheses?The 99% confidence interval include as a plausible value, so we would H0. We convincing evidence that the true mean hours of NREM sleep per night for adults who use a weighted blanket 5 hours. On the left, the image describes a study about sleep:- On average, adults spend approximately 5 hours per night in NREM (non-rapid eye movement) sleep.- The study involves selecting a random sample of adults and giving them each a weighted blanket to determine if it affects the mean hours of NREM sleep.- Hypotheses: - Null hypothesis \(H_0\): \(\mu = 5\) - Alternative hypothesis \(H_a\): \(\mu \neq 5\) - Here, \(\mu\) represents the true mean hours of NREM sleep per night for adults using a weighted blanket.A bullet point indicates:- A 99% confidence interval for the true mean NREM sleep hours for adults using a weighted blanket is (5.1, 5.8) hours.On the right, it addresses hypothesis testing based on the confidence interval:- The interval does not include 5 as a plausible value, so \(H_0\) would be rejected.- It suggests that there is convincing evidence that the mean NREM sleep hours for adults using a weighted blanket differs from 5 hours.

The 99% confidence interval for the the true mean hours of NREM sleep per night who use a weighted…

Answered: On average, adults spend approximately…

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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On average, adults spend approximately 5 hours per night in NREM (non-rapid eye movement) sleep. A sleep study selects a random sample of adults and gives them each a weighted blanket. They would like to know if using the weighted blanket changes the mean number of hours per night of NREM sleep. We want to test = 5 versus ≠ 5 where = the true mean hours of NREM sleep per night for adults who use a weighted blanket.

A 99% confidence interval for the true mean hours of NREM sleep per night for adults who use a weighted blanket is (5.1, 5.8) hours.

Based on the confidence interval, what conclusion would you make for a test of these hypotheses?

The 99% confidence interval include as a plausible value, so we would H₀. We convincing evidence that the true mean hours of NREM sleep per night for adults who use a weighted blanket 5 hours.

On the left, the image describes a study about sleep:

- On average, adults spend approximately 5 hours per night in NREM (non-rapid eye movement) sleep.
- The study involves selecting a random sample of adults and giving them each a weighted blanket to determine if it affects the mean hours of NREM sleep.
- Hypotheses:
- Null hypothesis \(H_0\): \(\mu = 5\)
- Alternative hypothesis \(H_a\): \(\mu \neq 5\)
- Here, \(\mu\) represents the true mean hours of NREM sleep per night for adults using a weighted blanket.

A bullet point indicates:

- A 99% confidence interval for the true mean NREM sleep hours for adults using a weighted blanket is (5.1, 5.8) hours.

On the right, it addresses hypothesis testing based on the confidence interval:

- The interval does not include 5 as a plausible value, so \(H_0\) would be rejected.
- It suggests that there is convincing evidence that the mean NREM sleep hours for adults using a weighted blanket differs from 5 hours.

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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