Answered: The effectiveness of a diet designed to…

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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The effectiveness of a diet designed to lower serum cholesterol is to be evaluated by measuring the cholesterol of 10 patients identified as being at risk for cardiovascular disease before and after being on the diet for 16 weeks. Use the data below to construct a two-sided 95% confidence interval for the mean difference. Give an interpretation of the confidence interval. You MUST show all your work to receive full credit. Partial credit is available.

Patient	Before Diet	After Diet
1	213	199
2	252	231
3	195	197
4	222	220
5	267	248
6	216	220
7	209	209
8	255	237
9	185	184
10	256	225

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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