Introduction to Statistical Quality Control
7th Edition
ISBN: 9781118146811
Author: Montgomery, Douglas C.
Publisher: John Wiley & Sons Inc
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Chapter 4, Problem 43E
The tensile strength of a paper product is related to the amount of hardwood in the pulp. Ten samples are produced in the pilot plant, and the data obtained are shown in Table 4E.9.
- (a) Fit a linear regression model relating strength to percentage hardwood.
TABLE 4E.9
Tensile Strength Data for Exercise 4.43
- (b) Test the model in part (a) for significance of regression.
- (c) Find a 95% confidence interval on the parameter β1.
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Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:
y = Retail PRICE (measured in dollars)
X1 = Microprocessor SPEED (measured in megahertz)
(Values in sample range from 10 to 40)
x 2 = CHIP size (measured in computer processing units)
(Values in sample range from 286 to 486)
A first-order regression model. was fit to the data. Part of the printout follows:
Parameter Estimates
T FOR 0
ERROR PARAMETER = 0 PROB>ITI
PARAMETER STANDARD
VARIABLE DF
ESTIMATE
INTERCEPT 1
-373.526392
1258.1243396 -0.297
0.7676
SPEED
1
104.838940
22.36298195 4 688
0.0001
сHP
1
3.571850
3.89422935
0.917
0.3629
Identify and interpret the estimate of B2-
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:
y = Retail PRICE (measured in dollars)
x1= Microprocessor SPEED (measured in megahertz)
(Values in sample range from 10 to 40)
x2 = CHIP size (measured in computer processing units)
(Values in sample range from 286 to 486)
A first-order regression model was fit to the data. Part of the printout follows:
Analysis of Variance
SOURCE
DF
MS
F VALUE
PROB>F
MODEL
2
34593103.008
17296051,504
19.018
0.0001
ERROR
57
51840202.926
909477.24431
C TOTAL
59
86432305.933
ROOT MSE
953.66516
3197.96667
R-SQUARE
0.4002
0.3792
DEP MEAN
CV.
ADJ R-SQ
29.82099
Test to determine if the model is adequate for predicting the price of a computer. Use a = .01.
The rental of an apartment (R) near campus is a function of the square
footage (Sq). A random sample of apartments near campus yielded the
following summary statistics:
R= $350, Sq = 100, sR = $ 30, and 8 są = 10. Suppose also that the
correlation between price and weight is 0.8.
(a) Write the implied least squares linear regression equation.
(b) Suppose an apartment has 75 sqft. Predict its price based on the
above model.
(c) Suppose the true rental of the apartment in part (b) is $ 325. What is
the value of the residual?
Chapter 4 Solutions
Introduction to Statistical Quality Control
Ch. 4 - Suppose that you are testing the following...Ch. 4 - Suppose that you are testing the following...Ch. 4 - Suppose that you are testing the following...Ch. 4 - Suppose that you are testing the following...Ch. 4 - Suppose that you are testing the following...Ch. 4 - Suppose that you are testing the following...Ch. 4 - The inside diameters of bearings used in an...Ch. 4 - The tensile strength of a fiber used in...Ch. 4 - The service life of a battery used in a cardiac...Ch. 4 - Using the data from Exercise 4.7, construct a 95%...
Ch. 4 - A new process has been developed for applying...Ch. 4 - A machine is used to fill containers with a liquid...Ch. 4 - Ferric chloride is used as a flux in some types of...Ch. 4 - The diameters of aluminum alloy rods produced on...Ch. 4 - The output voltage of a power supply is assumed to...Ch. 4 - Two machines are used for filling glass bottles...Ch. 4 - Two quality control technicians measured the...Ch. 4 - Suppose that x1N(,12) and x2N(2,22), and that x1...Ch. 4 - Two different hardening processes(1) saltwater...Ch. 4 - A random sample of 200 printed circuit boards...Ch. 4 - A random sample of 500 connecting rod pins...Ch. 4 - Two processes are used to produce forgings used in...Ch. 4 - A new purification unit is installed in a chemical...Ch. 4 - Two different types of glass bottles are suitable...Ch. 4 - The diameter of a metal rod is measured by 12...Ch. 4 - The cooling system in a nuclear submarine consists...Ch. 4 - An experiment was conducted to investigate the...Ch. 4 - Suppose we wish to test the hypotheses H0:=15H1:15...Ch. 4 - Consider the hypotheses H0:=0H1:0 where 2 is...Ch. 4 - Sample size allocation. Suppose we are testing the...Ch. 4 - Develop a test for the hypotheses H0: 1 = 2 H1: 1 ...Ch. 4 - Nonconformities occur in glass bottles according...Ch. 4 - An inspector counts the surface-finish defects in...Ch. 4 - An in-line tester is used to evaluate the...Ch. 4 - An article in Solid State Technology (May 1987)...Ch. 4 - Compare the mean etch uniformity values at each of...Ch. 4 - An article in the ACI Materials Journal (Vol. 84,...Ch. 4 - Compare the mean compressive strength at each...Ch. 4 - An aluminum producer manufactures carbon anodes...Ch. 4 - Plot the residuals from Exercise 4.36 against the...Ch. 4 - An article in Environmental International (Vol....Ch. 4 - An article in the Journal of the Electrochemical...Ch. 4 - The tensile strength of a paper product is related...Ch. 4 - A plant distills liquid air to produce oxygen,...Ch. 4 - Plot the residuals from Exercise 4.43 and comment...Ch. 4 - Plot the residuals from Exercise 4.44 and comment...Ch. 4 - The brake horsepower developed by an automobile...Ch. 4 - Analyze the residuals from the regression model in...Ch. 4 - Table 4E.11 contains the data from a patient...Ch. 4 - Analyze the residuals from the regression model on...Ch. 4 - Reconsider the patient satisfaction data in Table...Ch. 4 - Analyze the residuals from the multiple regression...Ch. 4 - Consider the Minitab output below. (a) Fill in the...Ch. 4 - Suppose that you are testing H0: 1 = 2 versus H1: ...Ch. 4 - Suppose that you are testing H0: = 2 versus H1: ...Ch. 4 - Consider the Minitab output below. (a) Fill in the...Ch. 4 - Consider the Minitab output shown below. (a) Is...Ch. 4 - Consider the Minitab output shown below. (a) Fill...Ch. 4 - Consider the Minitab output below. (a) Fill in the...Ch. 4 - Consider a one-way or single-factor ANOVA with...Ch. 4 - Consider the Minitab ANOVA output below. Fill in...
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardIf your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?arrow_forward
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