Answered: Calculate the sample estimate of the…

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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Question

Sleep deprivation tends to interfere with a person's ability to concentrate, learn, and remember things. Although the amount of sleep needed per night differs among people, the National Sleep Foundation's recommendation for teens is eight to ten hours of sleep per night. Suppose a study of sleep in 36 students randomly selected from Blue Lake College found that they were getting a mean of 6.8 hours of sleep per night, with a sample standard deviation of 1.2 hours per night.

a. Calculate the sample estimate of the standard error of the mean. Show all work.

b. Construct a 98% confident interval for the true population mean number of hours of sleep per night. Show all work.

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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