Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 7.1, Problem 7E
A chemical engineer is studying the effect of temperature and stirring rate on the yield of a certain product. The process is run 16 times, at the settings indicated in the following table. The units for yield are percent of a theoretical maximum.
| Temperature (°C) |
Stirring Rate (rpm) | Yield (%) |
| 110 | 30 | 70.27 |
| 110 | 32 | 72.29 |
| 111 | 34 | 72.57 |
| 111 | 36 | 74.69 |
| 112 | 38 | 76.09 |
| 112 | 40 | 73.14 |
| 114 | 42 | 75.61 |
| 114 | 44 | 69.56 |
| 117 | 46 | 74.41 |
| 117 | 48 | 73.49 |
| 122 | 50 | 79.18 |
| 122 | 52 | 75.44 |
| 130 | 54 | 81.71 |
| 130 | 56 | 83.03 |
| 143 | 58 | 76.98 |
| 143 | 60 | 80.99 |
- a. Compute the
correlation between temperature and yield, between stirring rate and yield, and between temperature and stirring rate. - b. Do these data provide good evidence that increasing the temperature causes the yield to increase, within the
range of the data? Or might the result be due to confounding? Explain. - c. Do these data provide good evidence that increasing the stirring rate causes the yield to increase, within the range of the data? Or might the result be due to confounding? Explain.
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A chemical engineer is studying the effect of temperature and stining rate on the yield of a
certain product. The process is run 16 times, at the settings indicated in the following table.
The units for yield are percent of a theoretical maximum.
Temperature (*C)
Stirring Rate (1pm)
Yield (%)
110
30
70.27
110
32
72.29
111
34
72.57
111
36
74.69
112
38
76.09
112
40
73.14
114
75.61
114
44
69.56
117
74.41
117
73.49
122
79.18
122
52
75.44
130
54
81.71
130
56
83.03
143
58
76.98
143
60
80.99
Compute the correlation between temperature and yield, between stinring rate and
yield, and between temperature and stiring rate.
Do these data provide good evidence that increasing the temperature causes the yield
to increase, within the range of the data? Or might the result be due to confounding?
Explain.
Do these data provide good evidence that increasing the stiring rate causes the yield to
increase, within the range of the data? Or might the result be due to confounding?
Explain.
a.
Б.
C.
A farmer in Indiana wants to examine the relation between the number of very hot days (days when the high
temperature exceeds 95° F) and the corn production of his farm (in bushels of corn per acre). He looks at
the data for 10 summers.
Let x¡ = the number of hot days during the ith summer.
%3D
= the corn production (in bushels per acre) during the ih summer.
Let yi
The data are in the table below:.
4
6.
7
8.
9.
10
i
2
14
10
7.
8.
1
12
Xi
Yi
95
80
83
87
88
85
99
102
79
95
a) Make a scatterplot of the data.
b) Examine your scatterplot and, without performing any calculations, EXPLAIN whether you expect
the correlation coefficient to be closer to -1, 0, or 1 and WHY.
c) Find the sample mean and standard deviation for each variable.
%3D
%3D
S.
%3D
y
d) Place an asterisk on your scatterplot at the point (x,ỹ).
Chapter 7 Solutions
Statistics for Engineers and Scientists
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