A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment,21subjects had a mean wake time of100.0min. After treatment, the21subjects had a mean wake time of78.1min and a standard deviation of24.4min. Assume that the21sample values appear to be from a normally distributed population and construct a95%confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of100.0min before the treatment? Does the drug appear to be effective?

Given information Sample size (n) = 21 After treatment Mean x̅ = 78.1 min Standard deviation (s) =…

Answered: A clinical trial was conducted to test…

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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A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment,

subjects had a mean wake time of

100.0

min. After treatment, the

subjects had a mean wake time of

78.1

min and a standard deviation of

24.4

min. Assume that the

sample values appear to be from a normally distributed population and construct a

95%

confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of

100.0

min before the treatment? Does the drug appear to be effective?

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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