Introduction to Statistical Quality Control
7th Edition
ISBN: 9781118146811
Author: Montgomery, Douglas C.
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4, Problem 37E
An article in the ACI Materials Journal (Vol. 84, 1987, pp. 213–216) describes several experiments investigating the rodding of concrete to remove entrapped air. A 3-in.-diameter cylinder was used, and the number of times this rod was used is the design variable. The resulting compressive strength of the concrete specimen is the response. The data are shown in Table 4E.5.
TABLE 4E.5
Compressive Strength Data for Exercise 4.37
- (a) Is there any difference in compressive strength due to the rodding level? Answer this question by using the analysis of variance with α = 0.05.
- (b) Construct box plots of compressive strength by rodding level. Provide a practical interpretation of these plots.
- (c) Construct a normal
probability plot of the residuals from this experiment. Does the assumption of anormal distribution for compressive strength seem reasonable?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
An article in the ACI Materials Journal (Vol. 84, 1987, pp. 213-216) describes several experiments investigating the rodding of concrete to
remove trapped air. A 3-inch x 6-inch cylinder was used, and the number of times this rod was used is the design variable. The resulting
compressive strength of the concrete specimen is the response. The data are shown in the following table.
...
Compressive Strength (psi)
Rodding Level
Observations
10
1530
1530
1440
15
1610
1650
1500
20
1560
1730
1530
25
1500
1490
1510
Calculate the test statistic fo.
Input answer up to 2 decimal places.
Test Statisticf =1.68
Blank 1
1.68
An article in the ACI Materials Journal (Vol. 84, 1987, pp. 213-216) describes several experiments investigating the rodding of concrete
to remove trapped air. A 3-inch x 6-inch cylinder was used, and the number of times this rod was used is the design variable. The
resulting compressive strength of the concrete specimen is the response. The data are shown in the following table.
Compressive Strength (psi)
Observations
Rodding Level
10
15
20
25
1530 1530 1440
1610 1650 1500
1560 1730 1530
1500 1490 1510
(a) Is there any difference in compressive strength due to the rodding level? Use a = 0.05.
Calculate to 2 decimal places for
Is there statistical evidence to say that rodding level affects compressive strength?
(b) Find to 2 decimal places the P-value for the F-statistic computed in part (a).
P-value=
(c) Analyze the following residual plots to determine model adequacy,
Does the assumption of normality seem reasonable?
Does there appear to be an outlier in the data?
Does the assumption…
An experiment was conducted to study the extrusion process of biodegradable packaging foam. Two of the factors considered for their effect on
the unit density (mg/ml) were the die temperature (145 °C vs. 155 °C) and the die diameter (3 mm vs. 4 mm). The results are stored in [Packaging
Foam 1]. Source: Data extracted from W. Y. Koh, K. M. Eskridge, and M. A. Hanna, "Supersaturated Split-Plot Designs," Journal of Quality
Technology, 45, January 2013, pp. 61-72.At the 0.05 level of significance,
3mm 4mm
57.22
145
72.54
145 53.60 66.70
145 48.13
49.28
145 69.89 44.14
145 62.78
58.37
145 55.18
53.98
155 57.50
63.03
155 54.17 46.73
155 73.86 60.17
155 90.28 46.78
155 88.19 43.27
155 82.61 56.93
Die Temperature
a. is there an interaction between die temperature and die diameter?
b. is there an effect due to die temperature?
c. is there an effect due to die diameter?
d. Plot the mean unit density for each die temperature for each die diameter.
e. What can you conclude about the effect of die…
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...
Additional Math Textbook Solutions
Find more solutions based on key concepts
How much time do Americans living in or near cities spend waiting in traffic, and how much does waiting in traf...
Business Statistics: A First Course (7th Edition)
The following set of data is from sample of n=5: a. Compute the mean, median, and mode. b. Compute the range, v...
Basic Business Statistics, Student Value Edition (13th Edition)
Error Type. Distinguish between random errors and systematic errors. How can we minimize the effects of random ...
Statistical Reasoning for Everyday Life (5th Edition)
Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis t...
Elementary Statistics: Picturing the World (7th Edition)
A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis. H0. is: the sample does not...
Introductory Statistics
Hamilton County Judges Hamilton County judges try thousands of cases per year. In an overwhelming majority of t...
Statistics for Business & Economics, Revised (MindTap Course List)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Pepsi Cans. In Exercises 5-8, refer to the axial loads (pounds) of aluminum Pepsi cans that are 0.0109 in. thick, as listed in Data Set 30 “Aluminum Cans” in Appendix B. An axial load of a can is the maximum weight supported by the side, and it is important to have an axial load high enough so that the can isn’t crushed when the top lid is pressed onto the top. There are seven measurements from each of 25 days of production. If the 175 axial loads are in one column, the first 7 are from the first day, the next 7 are from the second day, and so on, so that the “subgroup size” is 7. Pepsi Cans: R Chart Treat the seven measurements from each day as a sample and construct an R chart. What does the result suggest?arrow_forwardWild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.5 5.2 6.8 4.6 6.5 5.3 5.1 6.1 4.4 5.5 4.1 7.9 4.1 5.1 5.9 5.4 6.1 6.9 5.4 5.1 6.6 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 5% level of significance. (a) What is the level of significance?State the null and alternate hypotheses. Ho: ?1 = ?2 = ?3; H1: Exactly two means are equal.Ho: ?1 = ?2 = ?3; H1: Not all the means are equal. Ho: ?1 = ?2 = ?3; H1:…arrow_forwardWild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.9 5.5 6.7 4.1 6.8 5.8 5.2 6.5 4.5 5.4 4.5 7.2 4.1 5.4 5.2 5.2 6.2 6.9 5.6 5.2 6.7 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 10% level of significance. (a) What is the level of significance? 0.01 State the null and alternate hypotheses. O H,: H1 = H, = Hzi H;: All three means are different. O H,: H1 = H2 = Hzi H;: Exactly two means are equal. O H,: H, = H2 = Hai H,: At least two…arrow_forward
- Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.6 5.5 6.9 4.5 6.6 5.5 5.4 6.5 4.3 5.4 4.6 7.9 4.7 5.6 5.8 5.9 6.6 6.3 5.6 5.6 6.9 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 4 decimal places for MSBET, and MSW.) dfBET = dfW =…arrow_forwardWild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.5 5.2 6.7 4.4 6.5 5.7 5.2 6.9 4.1 5.9 4.4 7.8 4.3 5.5 5.7 5.3 6.4 6.1 5.8 5.5 6.9 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 10% level of significance. (a) What is the level of significance? (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = ? SSBET = ? SSW = ? Find d.f.BET, d.f.W, MSBET, and…arrow_forwardWild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.7 5.1 6.5 4.7 6.2 5.1 4.7 6.6 4.7 5.8 4.9 7.5 4.6 5.2 5.3 5.3 6.2 6.2 5.4 5.8 6.4 (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 4 decimal places for MSBET, and MSW.) dfBET = dfW = MSBET = MSW = Find the value of the sample F statistic. (Use 2 decimal places.)What are the degrees of freedom? (numerator) (denominator)arrow_forward
- Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.9 5.8 6.9 4.8 6.5 5.6 4.6 6.4 4.9 5.7 4.3 7.7 4.8 5.8 5.6 5.4 6.3 6.3 5.8 5.5 6.6 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 5% level of significance. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 4 decimal places for MSBET, and…arrow_forwardAn article in the Fire Safety Journal (“The Effect of Nozzle Design on the Stability and Performance of Turbulent Water Jets,” Vol. 4, August 1981) describes an experiment in which a shape factor was determined for several different nozzle designs at six levels of jet efflux velocity. Interest focused on potential differences between nozzle designs (blocks), with velocity considered as a nuisance variable. The data are shown below: Jet Efflux Velocity (m/s) Nozzle Design 11.73 14.37 16.59 20.43 23.46 28.74 1 0.78 0.80 0.81 0.75 0.77 0.78 2 0.85 0.85 0.92 0.86 0.81 0.83 3 0.93 0.92 0.95 0.89 0.89 0.83 4 1.14 0.97 0.98 0.88 0.86 0.83 5 0.97 0.86 0.78 0.76 0.76 0.75 1) Write the null hypothesis and the alternative hypothesis (for the factor). 2) Find the ANOVA table. (round to five decimal places). 3) What is your decision about the null hypothesis, consider ?. 4) If your decision in part (4) was reject , perform Tukey test to determine which pairwise means are…arrow_forwardA study is made of the effect of curing temperature on the compressive strength of a certain type of concrete. Five concrete specimens are cured at each of four temperatures, and the compressive strength of each specimen is measured (in MPa). The results are as follows: Temperature (°C) Strengths 31.2 29.6 30.8 30.0 31.4 10 30.0 27.7 31.1 31.3 30.6 20 35.9 36.8 35.0 34.6 36.5 30 38.3 37.0 37.5 36.1 38.4 Construct an ANOVA table. You may give a range for the P-value. Can you conclude that the mean strength differs with temperature? a. b.arrow_forward
- A) In the screenshot i provided B) Does either explanatory variable improve the fit of the model that uses the other? Use a test statistic for each. Use α=0.05.arrow_forward1P Unit Four Assessment SPR 24(1) - Protected View Saved V gn Layout References Mailings Review View Help Search em the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. MAT 120: Unit Four Test Name: Enable Editing Be sure to give CLEAR answers with explanation where is it appropriate. If you write your answers and upload a photo of your test, make CERTAIN that it is a clear photo and your writing is legible. 1. Determine the critical value, Za/2, that corresponds to the given level of confidence. (3 points each) a. 90% b. 84% I 2. A Rasmussen Reports national survey of U.S. adults reported that 22% dreaded exercising. The margin of error in the survey was 3.7%. What is the confidence interval for the true proportion of adults who dreaded exercising in this situation? Just give the interval. (6 points) 3. In a USA Today/Gallup poll, 834 out of 1024 randomly selected adult Americans aged 18 or older stated that a candidate's positions on the…arrow_forwardSuppose you fit the first-order model y = Po + B, x, + B2x2 + B3X3 + B,x4 + B5X5 + ɛ to n=28 data points and obtain SSE = 0.33 and R = 0.94. Complete parts a and b. a. Do the values of SSE and R suggest that the model provides a good fit to the data? Explain. A. Yes. Since R = 0.94 is close to 1, this indicates the model provides a good fit. Also, SSE = 0.33 is fairly small, which indicates the model provides a good fit. B. There is not enough information to decide. No. Since R = 0.94 is close to 1, this indicates the model does not provide a good fit. Also, SSE = 0.33 is fairly small, which indicates the model does not provide a good fit. b. Is the model of any use in predicting Test the null hypothesis Ho: B, = B2 = ... = B5 = 0 against the alternative hypothesis: At least of the %3D parameters B1, B2, B5 is nonzero. Use a = 0.05. The test statistic is (Round to two decimal places as needed.)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY