Construct a 95% confidence interval for the mean difference in their total ventilation when the subjectsare at rest and when performing imaginary muscular work if hypnosis is induced between the twophases.Do not use R. In a study of hypnotic suggestion, 16 male volunteers were randomly allocated to a treatment groupand a control group. Each subject participated in a two-phase experimental session. In the first phase,respiration was measured while the subject was awake and at rest. In the second phase, the subjectwas told to imagine that he was performing muscular work, and respiration was measured again. Forsubjects in the treatment group, hypnosis was induced between the first and second phases; thus, thesuggestion to imagine muscular work was "hypnotic suggestion" for treatment subjects and "wakingsuggestion" for control subjects. The table below shows the measurements of total ventilation (litersof air per minute per square meter of body area) for all 16 subjects.Treatment GroupTotal VentilationSubject12345678MeanSDDifferenceRest Work (Work-Rest)5.746.795.327.185.606.066.326.346.249.077.7716.466.958.1411.728.066.16875 9.301250.62109 3.322760.502.282.459.281.352.085.401.723.13252.8620Control GroupTotal VentilationSubject Rest Work96.21.5.50104.504.64114.864.61124.78p134.793.785.415.32145.70155.414.54166.085.98Mean 5.29125 4.9725SD0.65160 0.7027Difference(Work-Rest)-0.710.14-0.25-1.000.62-0.38-0.87-0.10-0.318750.54368

Treatment group Control group Total ventilation Difference Total ventilation Difference…

Answered: Construct a 95% confidence interval for…

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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Question

Construct a 95% confidence interval for the mean difference in their total ventilation when the subjects
are at rest and when performing imaginary muscular work if hypnosis is induced between the two
phases.
Do not use R.

In a study of hypnotic suggestion, 16 male volunteers were randomly allocated to a treatment group
and a control group. Each subject participated in a two-phase experimental session. In the first phase,
respiration was measured while the subject was awake and at rest. In the second phase, the subject
was told to imagine that he was performing muscular work, and respiration was measured again. For
subjects in the treatment group, hypnosis was induced between the first and second phases; thus, the
suggestion to imagine muscular work was "hypnotic suggestion" for treatment subjects and "waking
suggestion" for control subjects. The table below shows the measurements of total ventilation (liters
of air per minute per square meter of body area) for all 16 subjects.
Treatment Group
Total Ventilation
Subject
1
2
3
4
5
6
7
8
Mean
SD
Difference
Rest Work (Work-Rest)
5.74
6.79
5.32
7.18
5.60
6.06
6.32
6.34
6.24
9.07
7.77
16.46
6.95
8.14
11.72
8.06
6.16875 9.30125
0.62109 3.32276
0.50
2.28
2.45
9.28
1.35
2.08
5.40
1.72
3.1325
2.8620
Control Group
Total Ventilation
Subject Rest Work
9
6.21.
5.50
10
4.50
4.64
11
4.86
4.61
12
4.78
p
13
4.79
3.78
5.41
5.32
14
5.70
15
5.41
4.54
16
6.08
5.98
Mean 5.29125 4.9725
SD
0.65160 0.7027
Difference
(Work-Rest)
-0.71
0.14
-0.25
-1.00
0.62
-0.38
-0.87
-0.10
-0.31875
0.54368

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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