E1C04 09/14/2010
14:7:49 Page 157
4.28 An engineer measures the diameter of 20 tubes selected at random from a large shipment. The sample
yields: x ¼ 47:5 mm and s x ¼ 8.4 mm. The manufacturer of the tubes claims that x
0
¼ 42.1 mm.
What can the engineer conclude about this claim?
4.29 In manufacturing a particular set of motor shafts, only shaft diameters of between 38.10 and 37.58
mm are usable. If the process mean is found to be 37.84 mm with a standard deviation of 0.13 mm,
what percentage of the population of manufactured shafts are usable?
For Problems 4.30 through 4.33, it would be helpful to use a least-squares software package, such
as Polynomial_fit, or the least-squares analytical capability of spreadsheet software.
4.30 Determine the static sensitivity for the following data by using a least-squares regression analysis.
Plot the data and fit including the 95% confidence interval due to random scatter about the fit.
Compare the uncertainty interval estimated by Equation 4.37 with that of Equation 4.39 and discuss
the differences.
Y:
2.7
3.6
4.4
5.2
9.2
X:
0.4
1.1
1.9
3.0
5.0
4.31 Using the following data, determine a suitable least-squares fit of the data. Which order polynomial
best fits this data set? Plot the data and the fit with 95% confidence interval on an appropriate graph.
Y:
1.4
4.7
17.3
82.9
171.6
1227.1
X:
0.5
1.1
2.0
2.9
5.1
10.0
4.32 The following data have the form y ¼ ax
b . Plot the data and their best fit with 95% confidence
interval. Estimate the static sensitivity at each value of X.
Y:
0.14
2.51
15.30
63.71
X:
0.5
2.0
5.0
10.0
4.33 A fan performance test yields the following data:
Q:
2000
6000
10000
14000
18000
22000
h:
5.56
5.87
5.73
4.95
3.52
1.08
where Q is flow rate in m
3 /s and h is static head in cm-H 2 O. Find the lowest-degree polynomial that
best fits the data as h ¼ f(Q). Note: Physically, a second-order polynomial is a reasonable fit. Explain
your choice.
4.34 A camera manufacturer purchases glass to be ground into lenses. From experience it is known that
the variance in the refractive index of the glass is 1.25 Â 10
À4 . The company will reject any shipment
of glass if the sample variance of 30 lenses measured at random exceeds 2.10 Â 10
À4 . What is the
probability that such a batch of glass will be rejected even though it is actually within the normal
variance for refractive index?
4.35 The setup for grinding a type of bearing is considered under control if the bearings have a mean
diameter of 5.000 mm. Normal procedure is to measure 30 bearings each 10 minutes to monitor
Problems 157
14:7:49 Page 157
4.28 An engineer measures the diameter of 20 tubes selected at random from a large shipment. The sample
yields: x ¼ 47:5 mm and s x ¼ 8.4 mm. The manufacturer of the tubes claims that x
0
¼ 42.1 mm.
What can the engineer conclude about this claim?
4.29 In manufacturing a particular set of motor shafts, only shaft diameters of between 38.10 and 37.58
mm are usable. If the process mean is found to be 37.84 mm with a standard deviation of 0.13 mm,
what percentage of the population of manufactured shafts are usable?
For Problems 4.30 through 4.33, it would be helpful to use a least-squares software package, such
as Polynomial_fit, or the least-squares analytical capability of spreadsheet software.
4.30 Determine the static sensitivity for the following data by using a least-squares regression analysis.
Plot the data and fit including the 95% confidence interval due to random scatter about the fit.
Compare the uncertainty interval estimated by Equation 4.37 with that of Equation 4.39 and discuss
the differences.
Y:
2.7
3.6
4.4
5.2
9.2
X:
0.4
1.1
1.9
3.0
5.0
4.31 Using the following data, determine a suitable least-squares fit of the data. Which order polynomial
best fits this data set? Plot the data and the fit with 95% confidence interval on an appropriate graph.
Y:
1.4
4.7
17.3
82.9
171.6
1227.1
X:
0.5
1.1
2.0
2.9
5.1
10.0
4.32 The following data have the form y ¼ ax
b . Plot the data and their best fit with 95% confidence
interval. Estimate the static sensitivity at each value of X.
Y:
0.14
2.51
15.30
63.71
X:
0.5
2.0
5.0
10.0
4.33 A fan performance test yields the following data:
Q:
2000
6000
10000
14000
18000
22000
h:
5.56
5.87
5.73
4.95
3.52
1.08
where Q is flow rate in m
3 /s and h is static head in cm-H 2 O. Find the lowest-degree polynomial that
best fits the data as h ¼ f(Q). Note: Physically, a second-order polynomial is a reasonable fit. Explain
your choice.
4.34 A camera manufacturer purchases glass to be ground into lenses. From experience it is known that
the variance in the refractive index of the glass is 1.25 Â 10
À4 . The company will reject any shipment
of glass if the sample variance of 30 lenses measured at random exceeds 2.10 Â 10
À4 . What is the
probability that such a batch of glass will be rejected even though it is actually within the normal
variance for refractive index?
4.35 The setup for grinding a type of bearing is considered under control if the bearings have a mean
diameter of 5.000 mm. Normal procedure is to measure 30 bearings each 10 minutes to monitor
Problems 157