A group of six individuals with high cholesterol levels were given a new diet designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after the implementation of the diet for each individual, with the following results:BeforeAfter227160234174257178269170218178248178A dietician claims that the mean reduction in cholesterol level is 51 milligrams per deciliter. Find the 98% confidence interval for the mean reduction in cholesterol level. Interpret the results. Does the 98% confidence interval contradict this claim?

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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 group of six individuals with high cholesterol levels were given a new diet designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after the implementation of the diet for each individual, with the following results:

Before	After
227	160
234	174
257	178
269	170
218	178
248	178

A dietician claims that the mean reduction in cholesterol level is 51 milligrams per deciliter. Find the 98% confidence interval for the mean reduction in cholesterol level. Interpret the results. Does the 98% confidence interval contradict this claim?

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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