Answered: The design of controls and instruments…

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

The design of controls and instruments affects how easily people can use them. A student project investigated this effect by asking 25 right handed students to turn a knob with their right hands that moved an indicator by screw action. There were two identical instruments, one with a right-hand thread and the other with a left-hand thread. The table given has the data from the student project.
1. Calculate and interpret a 90% confidence interval for the mean time advantage of right hand over left hand threads in the setting above.

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1
Subject
1
2
3
4
5
6
7
8
9
10
11
12
13
HARG
14
15
16
17
18
19
20
21
22
23
24
25
n
A
1
[台
Right hand
threads (sec)
113
105
130
101
138
118
87
116
75
96
122
103
116
107
118
103
111
104
111
89
78
100
89
85
88
3
2
100%
Left hand
threads (sec)
137
105
133
108
115
170
103
145
78
107
84
148
147
87
166
146
123
135
112
93
76
116
78
101
123

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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