A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a sample standard deviation of 42.3 min (based on data from “Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults,” by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min.State the null hypothesis (H0).State the alternative hypothesis (H1).What kind of test would this be, a two-tailed, a left-tailed, or a right-tailed?Sketch a normal distribution curve and highlight the region of significance (also called critical region or rejection region).What test statistic is most relevant to this test? Why?\Use Excel to determine the P-value. What is it?On your graph, next highlight the P-value.State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)Next, test this hypothesis using the critical value method.Using the most relevant test statistic, find the critical value from the tables at the back of the textbook. What is it?Sketch a normal distribution curve, plot the critical value, and highlight the critical or rejection region.Using the formulas in section 8-3, calculate the test statistic based on the sample data. Show your work. What is the test statistic?On your graph, plot the test statistic.State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)Does zopiclone appear to be effective? Why do you think so?

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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 the drug zopiclone for treating insomnia in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a sample standard deviation of 42.3 min (based on data from “Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults,” by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min.

State the null hypothesis (H0).
State the alternative hypothesis (H1).
What kind of test would this be, a two-tailed, a left-tailed, or a right-tailed?
Sketch a normal distribution curve and highlight the region of significance (also called critical region or rejection region).
What test statistic is most relevant to this test? Why?\
Use Excel to determine the P-value. What is it?
On your graph, next highlight the P-value.
State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

Next, test this hypothesis using the critical value method.
Using the most relevant test statistic, find the critical value from the tables at the back of the textbook. What is it?
Sketch a normal distribution curve, plot the critical value, and highlight the critical or rejection region.
Using the formulas in section 8-3, calculate the test statistic based on the sample data. Show your work. What is the test statistic?
On your graph, plot the test statistic.
State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)
Does zopiclone appear to be effective? Why do you think so?

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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