Answered: 9.65 Suppose the investigators are…

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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9.65 Suppose the investigators are reluctant to assume
that the change in LVM over four years is normally distributed. What test can be used to assess if there is a change
in mean LVM over four years?
9.66 What are the hypotheses being tested with this test?
9.67 What is the test statistic for this test as applied to the
data in Table 9.18?
Hint: Assume that the large sample method of significance
testing is valid for these data, despite the n = 10

TABLE 9.18 Pilot data on left ventricular mass
(LVM) in children from the Bogalusa
Heart Study
ID
Baseline
Change (g)*
LVM (g)
4-year
LVM (g)
1
139
163
24
134
126
-8
86
142
56
4
98
96
-2
78
111
33
6.
90
108
18
7
102
167
65
8.
73
82
9
93
77
-16
10
162
172
10
*4-year LVM minus baseline LVM

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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