Answered: Healthy Sleep Duration The centers 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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Healthy Sleep Duration

The centers for Disease Control and Prevention, CDC, defines a healthy sleep duration to be at least seven hours per day. The CDC reports that the percentage of people who report a healthy sleep duration varies by marital status. The CDC also reports that in 2018, 67% of those who are married report a healthy sleep duration; 62% of those who have never been married report a healthy sleep duration; and 56% of those who are divorced, widowed, or separated report a healthy sleep duration. The file Sleep Habits contains sample data on the sleeping habits of people who have never been married that are consistent with the CDC’s findings. Use this data to answer the following questions.

Develop a point estimate and a 95% confidence interval for the proportion of those who have never been married who report a healthy sleep duration.

Develop a point estimate and a 95% confidence interval for the mean number of hours of sleep for those who have never been married.

For those who have never been married, estimate the number of hours of sleep per day for those who report a healthy sleep duration.

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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