The article “An Investigation into the Ball Burnishing of Aluminium Alloy 6061-T6” (M. El-Axir. J Engineering Manufacture. 2007:1733–1742) presents the results of study that investigated the effects of three burnishing factors on the reduction in diameter of the workpiece (in μm). The factors are A: Burnishing speed, B: Burnishing force, and C: Burnishing feed. The results presented in the following table form a 23 factorial design (some additional results are omitted).
- a. Compute estimates of the main effects and the interactions.
- b. Is it possible to compute an error sum of squares? Explain.
- c. Arc any of the interactions among the larger effects? If so, which ones?
- d. Someone claims that the additive model holds. Do the results tend to support this statement? Explain.
Want to see the full answer?
Check out a sample textbook solutionChapter 9 Solutions
Statistics for Engineers and Scientists
Additional Math Textbook Solutions
Introductory Statistics
Statistics: The Art and Science of Learning from Data (4th Edition)
Introductory Statistics (10th Edition)
Elementary Statistics: Picturing the World (6th Edition)
Business Statistics: A First Course (7th Edition)
Introduction to Statistical Quality Control
- Can you help with parts iv, v, and vi please? The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. The paper ("Left atrial size increases with body mass index in children")[https://www.ncbi.nlm.nih.gov/pubmed/19147240] (International Journal of Cardiology [2009]) described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on this data, the authors concluded that for healthy children, the left atrial diameter was approximately normally distributed with a mean of 26.4 mm and a standard deviation of 4.2 mm. i) Use `plotDist` to draw the probability density function of the left atrial diameter. ii) Generate 50 sample measurements of the left atrial diameters and plot the measurements using a histogram. iii) Approximately what proportion of healthy children have left atrial diameters less than…arrow_forwardThe article “An Ivestigation into the Ball Burnishing of Aluminium Alloy 6061-T6" (M. El-Axir, J Engineering Manufacture, 2007:1733-1742) presents the results of study that investigated the effects of three bumishing factors on the reduction in diameter of the workpiece (in um). The factors are A: Bumishing speed, B: Burnishing force, and C: Bumishing feed. The results presented in the following table form a 23 factorial design (some additional results are omitted). Reduction 570 A -1 -1 -1 -1 -1 353 -1 778 -1 769 -1 544 -1 319 -1 651 625 Compute estimates of the main effects and the interactions. b. Is it possible to compute an error sum of squares? Explain. Are any of the interactions among the larger effects? If so, which ones? d. Someone claims that the additive model holds. Do the results tend to support this statement? Explain.arrow_forwardThe Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and 84 preserved Etruscan male skulls was analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, “The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones.” In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O’Connor, eds., Little, Brown&Co., 1959] a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples. b. Based on your results from part (a), which would you be inclined to use to…arrow_forward
- 1) Malaria is a disease that destroys red blood cells (the parasite invades red blood cells, multiplies, and then infects more red blood cells). In a recent study (Kotepul, et al., 2015) looking at various blood counts, the authors found the following results. Results are in billion red blood cells / cubic mm. Note that I have deliberately modified these results (do not use R): n ̄y s Low infection 527 4.16 2.23 High infection 157 4.51 2.34 Is there a difference in red blood cell count?(Hint: please think about this before you just start working on the problem!)arrow_forwardThe article "Mathematical Modeling of the Argon-Oxygen Decarburization Refining Process of Stainless Steel: Part II. Application of the Model to Industrial Practice" (J. Wei and D. Zhu, Metallurgical and Materials Transactions B, 2001:212-217) presents the carbon content (in mass %) and bath temperature (in K) for 32 heats of austenitic stainless steel. These data are shown in the following table. Carbon % Temp. 1975 19 23 1947 22 1954 16 1992 17 1965 18 1971 12 2046 24 1945 17 1984 20 1991arrow_forward17.7 Butterfly wings. Researchers studied the morphological attributes of monarch butterflies (Danaus plexippus), a species that undertakes large seasonal migrations over North America. They measured the forewing weight (in milligrams, mg) of a sample of 92 monarch butterflies, all of which had been reared in captivity in identical conditions.° Figure 17.4 shows the output from the statistical software JMP. (The data are also available in the Large.Butterfly the data file if you wish to practice working with your own software.) Estimate with 95% confidence the mean forewing weight of monarch butterflies reared in captivity. Follow the four- step process as illustrated in Example 17.2. 4 STEP そMP FWweight 30 25 20 15 10 11 12 13 14 15 8 9 10 Summary Statistics Mean 11.795652 Std Dev 1.1759413 Std Err Mean 0.1226004 Upper 95% Mean Lower 95% Mean 1 FIGURE 17.4 Software output (JMP) for the forewing weight of monarch 12.039183 11.552122 92 N. butterflies. Countarrow_forward
- A Civil engineer involved in construction requires 1100, 2100 and 1600 m3 of sand, fine gravel and coarse gravel for a building project. There are three pits from which these materials can be obtained. The composition of these pits is PIT # SAND % FINE GRAVEL % COARSE GRAVEL % 1 52 30 18 20 50 30 3 25 20 55 How many cubic meters must be hauled from PIT 2 in order to meet the engineer's needs? Round-off to 4 decimal places Use GAUSS-JACOBI METHODarrow_forwardInterpret effect size t(30)=1.12, p=.34, n2=.001 small, medium, or largearrow_forwardH.W. 1 Given that zl = 3 + 4i, z2 = 1 – 2i, calculate: %3D 1. z1 – 2; 2. 3. |z1|; 4. 2. 5. zl+3 6. 2* z2arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage