An herbal medicine is tested on 10 patients with sleeping disorders. The table below shows the hours of sleep patients got during one night without using the herbal medicine and the hours of sleep the same patients got on another night after the herbal medicine was administered. Assume underlying normal distributions. Patient 1 2 3 4 5 6 7 8 9 10 Hours without 1.0 1.4 3.4 3.7 5.1 5.1 5.2 5.3 5.5 5.8 Hours with 2.9 3.3 3.5 4.4 5.0 5.0 5.2 5.3 6.0 6.5 Construct a 90% confidence interval for the mean difference. Interpret the confidence interval. What is the point estimate of this interval? What is the margin of error? At a= 0.01, does the herbal medicine increase the number of hours of sleep during one night?

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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An herbal medicine is tested on 10 patients with sleeping disorders. The table below shows the hours of sleep patients got during one night without using the herbal medicine and the hours of sleep the same patients got on another night after the herbal medicine was administered. Assume underlying normal distributions.

Patient	1	2	3	4	5	6	7	8	9	10
Hours without	1.0	1.4	3.4	3.7	5.1	5.1	5.2	5.3	5.5	5.8
Hours with	2.9	3.3	3.5	4.4	5.0	5.0	5.2	5.3	6.0	6.5

Construct a 90% confidence interval for the mean difference.

Interpret the confidence interval.

What is the point estimate of this interval?

What is the margin of error?

At a= 0.01, does the herbal medicine increase the number of hours of sleep during one night?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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