Question
In: Statistics and Probability
An article reported the following data on oxidation-induction time (min) for various commercial oils: 88 104...
An article reported the following data on oxidation-induction time (min) for various commercial oils: 88 104 130 160 180 195 132 145 213 105 145 151 153 136 87 99 95 119 129 (a) Calculate the sample variance and standard deviation. (Round your answers to three decimal places.) s2 = min2 s = min (b) If the observations were reexpressed in hours, what would be the resulting values of the sample variance and sample standard deviation? Answer without actually performing the reexpression. (Round your answer to three decimal places.) s2 = hr2 s = hr
Solutions
Expert Solution
Sol:
| X | X - mean | (X-mean)2 | X2 |
| 88 | -47.0526 | 2213.95014 | 7744 |
| 104 | -31.0526 | 964.265928 | 10816 |
| 130 | -5.05263 | 25.5290859 | 16900 |
| 160 | 24.94737 | 622.371191 | 25600 |
| 180 | 44.94737 | 2020.26593 | 32400 |
| 195 | 59.94737 | 3593.68698 | 38025 |
| 132 | -3.05263 | 9.31855956 | 17424 |
| 145 | 9.947368 | 98.9501385 | 21025 |
| 213 | 77.94737 | 6075.79224 | 45369 |
| 105 | -30.0526 | 903.160665 | 11025 |
| 145 | 9.947368 | 98.9501385 | 21025 |
| 151 | 15.94737 | 254.31856 | 22801 |
| 153 | 17.94737 | 322.108033 | 23409 |
| 136 | 0.947368 | 0.89750693 | 18496 |
| 87 | -48.0526 | 2309.0554 | 7569 |
| 99 | -36.0526 | 1299.79224 | 9801 |
| 95 | -40.0526 | 1604.2133 | 9025 |
| 119 | -16.0526 | 257.686981 | 14161 |
| 129 | -6.05263 | 36.634349 | 16641 |
| 2566 | -2.8E-14 | 22710.9474 | 369256 |
s^2=sample variance=22710.9474/19-1=1261.719 min^2
s=sample standard deviation=sqrt(1261.719)=35.521 min
Solutionb:
1 hour=60 min
1min=1/60 hr
s^2=sample variance=22710.9474/19-1=1261.719 min^2=1261.719 (1/60 )^2hr^2=0.3504775=0.350 hour^2
s=sample standard deviation=sqrt(1261.719)=35.521 min=35.521/60=0.5920167 hour=0.592 hour
orchestra answered 1 year agoRelated Solutions
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x
100
125
125
150
150
200
200
250
250
300
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y
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150
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200
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article on nitrogen emissions, with x = burner area
liberation rate (MBtu/hr-ft2) and y =
NOx emission rate (ppm):
x
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125
125
150
150
200
200
250
250
300
300
350
400
400
y
140
140
190
200
190
310
290
410
420
450
400
600
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(a) Assuming that the simple linear regression model is valid,
obtain the least squares estimate of the true regression line.
(Round...
The following data is representative of that reported in an article on nitrogen emissions, with x...
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article on nitrogen emissions, with x = burner area
liberation rate (MBtu/hr-ft2) and y =
NOx emission rate (ppm):
x
100
125
125
150
150
200
200
250
250
300
300
350
400
400
y
150
130
190
220
190
330
280
400
420
430
400
590
610
680
(a) Assuming that the simple linear regression model is valid,
obtain the least squares estimate of the true regression line.
(Round...
The following data is representative of that reported in an article on nitrogen emissions, with x...
The following data is representative of that reported in an
article on nitrogen emissions, with x = burner area
liberation rate (MBtu/hr-ft2) and y =
NOx emission rate (ppm):
x
100
125
125
150
150
200
200
250
250
300
300
350
400
400
y
140
140
170
210
200
330
280
390
440
450
400
590
610
660
(a) Assuming that the simple linear regression model is valid,
obtain the least squares estimate of the true regression line.
(Round...
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article with x = burner-area liberation rate (MBtu/hr-ft2) and y =
NOx emission rate (ppm): x 100 125 125 150 150 200 200 250 250 300
300 350 400 400 y 150 140 170 210 180 320 280 400 420 440 400 590
620 680 (a) Does the simple linear regression model specify a
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article with x = burner-area liberation rate
(MBtu/hr-ft2) and y = NOx
emission rate (ppm):
x
100
125
125
150
150
200
200
250
250
300
300
350
400
400
y
150
150
180
210
180
310
280
410
440
430
400
610
610
680
(a) Does the simple linear regression model specify a useful
relationship between the two rates? Use the appropriate test
procedure to obtain information about the...
The following data is representative of that reported in an article with x = burner-area liberation...
The following data is representative of that reported in an
article with x = burner-area liberation rate
(MBtu/hr-ft2) and y = NOx
emission rate (ppm):
x
100
125
125
150
150
200
200
250
250
300
300
350
400
400
y
140
150
170
220
200
330
290
400
420
430
390
610
600
660
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