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Name: The following table gives the BMI (in kg/m22) and some summary statist
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Description: The following table gives the BMI (in kg/m22) and some summary statistics for ten randomly sampled patients who participated in a 12-week program to improve their lifestyle through proper diet and physical training. (Credit: Liu. L. Chapter 4 -- Bios

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The following table gives the BMI (in kg/m22) and some summary statistics for ten randomly sampled patients who participated in a 12-week program to improve their lifestyle through proper diet and physical training. (Credit: Liu. L. Chapter 4 -- Biostatistical Basis of Inference in Heart Failure Study. Heart Failure: Epidemiology and Research Methods).

Given that a preliminary analysis reveals that the variable of interest is normally distributed, complete the following exercises:

Compute a 90% confidence interval for the mean difference in average BMI between Week 0 and Week 12.
At the 10% significance level will the corresponding two-sided hypothesis test about the mean difference result in rejection of H0H0? Explain based on your result from a.No calculation is required.

The following table gives the BMI (in kg/m22) and some summary statistics for ten randomly
sampled patients who participated in a 12-week program to improve their lifestyle through proper
diet and physical training. (Credit: Liu. L. Chapter 4 -- Biostatistical Basis of Inference in Heart
Failure Study. Heart Failure: Epidemiology and Research Methods).
Patient
Patient
Patient
Patient
Patient
Patient
Patient
Patient
Patient
Patient
Standard
Week
Mean
1
2
3
5
6
8.
10
Deviation
Week 0
35
32
27
26
33
28
26
28
33
30
21 = 29.8
$1 = 3.26
Week 12
37
26
28
24
27
26
23
27
27
24
2z = 26.9
82 = 3.9
Differences
2
-6
-2
-6
-2
-4
-1
-6
-6
i = -2.9
S= 3.03
Given that a preliminary analysis reveals that the variable of interest is normally distributed,
complete the following exercises:
a. Compute a 90% confidence interval for the mean difference in average BMI between Week 0 and
Week 12.
b. At the 10% significance level will the corresponding two-sided hypothesis test about the mean
difference result in rejection of HoH0? Explain based on your result from a. No calculation is
required.

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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