Concept explainers
A study of the properties of metal plate-connected trusses used for roof support (“Modeling Joints Made with Light-Gauge Metal Connector Plates,” Forest Products J., 1979: 39–44) yielded the following observations on axial-stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in:
4: | 309.2 | 409.5 | 311.0 | 326.5 | 316.8 | 349.8 | 309.7 |
6: | 402.1 | 347.2 | 361.0 | 404.5 | 331.0 | 348.9 | 381.7 |
8: | 392.4 | 366.2 | 351.0 | 357.1 | 409.9 | 367.3 | 382.0 |
10: | 346.7 | 452.9 | 461.4 | 433.1 | 410.6 | 384.2 | 362.6 |
12: | 407.4 | 441.8 | 419.9 | 410.7 | 473.4 | 441.2 | 465.8 |
Does variation in plate length have any effect on true average axial stiffness? State and test the relevant hypotheses using analysis of variance with a 5 .01. Display your results in an ANOVA table. [Hint:
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Chapter 10 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
- A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 321.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 439.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 390.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 402.4 441.8 419.9 410.7 473.4 441.2 465.8 USE SALT Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. ○ Ho: H₁ = H₂ = H3 = H4=H5 Ha: all five u's are unequal O Ho: H₁ H₂ H3 H4 H5 Ha: all five μ's are equal Ho H₁ = ₂ = 3 = H4 = 5 H₂: at least two μ's are unequal Ho: H₁ H₂ H3 H4 H5 Ha: at least two μ's are equal Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Mean Degrees of Sum of freedom Squares Squares Source Treatments…arrow_forwardA study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 323.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 423.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 393.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 418.4 441.8 419.9 410.7 473.4 441.2 465.8 Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: at least two ?i's are equalH0: ?1 = ?2 = ?3 = ?4 = ?5Ha: all five ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 = ?5Ha: at least two ?i's are unequalH0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: all five ?i's are equal Test the relevant hypotheses using analysis of variance with ? = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Source Degrees offreedom Sum…arrow_forwardQ.2. Because of potential variability in aging due to different castings and segments on the castings, a Latin square design with N=7 was used to investigate the effect of heat treatment on aging. With A= castings, B = Σχ = 297,216.90, segments, C = heat treatments, summary statistics include x... = 3815.8, Σχ = 297,155.01, and 297,200.64, = 297,317.65. Obtain the ANOVA table and test at level .05 the hypothesis that heat treatment has no effect on aging.arrow_forward
- Q1 A) List down the measures of central tendency and measures of dispersion 2) The operations manager of a plant that manufactures tires wants to compare the actual inner diameters of two grades of tires, each of B) which is expected to be 575 millimeters. A sample of five tires of each grade was selected, and the results representing the inner diameters of the tires, ranked from smallest to largest, are as follows. Grade X grade Y 568 570 575 578 584 573 574 575 577 578 requirement. a) for each of the tow grades of tries, compute the mwan, median, and standred deviation. b) which grade of tire providing better quality? explain. c) what would be the effect on your answer in (a) and (b) if the last value for grade Y were 588 insert 578 explain. C) The file contins the overall miles per gallon (MPG) OF 2010 family sedan: 24 21 22 23 24 34 34 34 20 20 22 22 44 32 20 20 22 20 39 20 Source:…arrow_forwardThe article "Electrical Impedance Variation with Water Saturation in Rock" (Q. Su, Q. Feng, and Z. Shang, Geophysics, 2000:68–75) reports measurements of permeabilities (in 10-3um?), porosities (in percent), and surface area per unit volume of pore space (in 104 cm -1) for several rock samples. The results are presented in the following table, denoting In Permeability by y, porosity by x1, and surface area per unit volume by x2. y -0.27 х, 19.83 X2 9.55 2.58 17.93 10.97 3.18 21.27 31.02 1.70 18.67 28.12 -1.17 7.98 52.35 -0.27 10.16 32.82 17.86 13.48 -0.53 57.66 -0.29 21.10 4.94 17.49 9.15 1.94 14.18 11.72 3.74 23.88 5.43 0.58 10.52 20.03 -0.56 18.92 13.10 -0.49 18.55 12.78 -0.01 13.72 40.28 -1.71 9.12 53.67 14.39 11.38 -0.12 26.75 -0.92 75.62 2.18 16.59 9.95 4.46 16.77 7.88 2.11 18.55 88.10 -0.04 18.02 10.95 Fit the model y = 6, + B,X1 + B>x2 + B3x;xX2 + ɛ. Compute the analysis of variance table. a. b. Fit the model y = Bo + B;X1 + B2X2 + ɛ. Compute the analysis of variance table. c.…arrow_forwardMetal conduits or hollow pipes are used in electrical wiring. In testing 1-inch pipes, these data are obtained on the outside diameter (in inches) of the pipe: 1.2811.2931.2871.2861.2881.2931.2911.2951.2921.2911.2901.2961.2891.2891.2861.2911.2911.2881.2891.286 Assume that the sampling is from a normal distribution. Find a 95% confidence interval on the mean outside diameter of pipes of this type.arrow_forward
- ONLY THE LAST ONE Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type. 5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.5 6.8 6.5 7.0 6.3 7.9 9.0 8.4 8.7 7.8 9.7 7.4 7.7 9.7 8.2 7.7 11.6 11.3 11.8 10.7 The data below give accompanying strength observations for cylinders. 6.5 5.8 7.8 7.1 7.2 9.2 6.6 8.3 7.0 8.3 7.8 8.1 7.4 8.5 8.9 9.8 9.7 14.1 12.6 11.9 Prior to obtaining data, denote the beam strengths by X1, . . . , Xm and the cylinder strengths by Y1, . . . , Yn. Suppose that the Xi's constitute a random sample from a distribution with mean μ1 and standard deviation σ1 and that the Yi's form a random sample (independent of the Xi's) from another distribution with mean μ2 and standard deviation σ2. (a) Use rules of expected value to show that X − Y is an unbiased estimator of μ1 − μ2. E(X − Y) = E(X) − E(Y) = μ1 − μ2 E(X − Y) = E(X) − E(Y) 2 = μ1 − μ2 E(X − Y) = nm E(X) − E(Y) = μ1 − μ2 E(X −…arrow_forwardQ1A) List down the measures of central tendency and measures of dispersion 1) Q1B) The operations manager of a plant that manufactures tires wants to compare the actual inner diameters of two grades of tires, each of which is expected to be 575 millimeters. A sample of five tires of each grade was selected, and the results representing the inner diameters of the tires, ranked from smallest to largest, are as follows. Grade X grade Y 568 570 575 578 584 573 574 575 577 578 requirement. a) for each of the tow grades of tries, compute the mwan, median, and standred deviation. b) which grade of tire providing better quality? explain. c) what would be the effect on your answer in (a) and (b) if the last value for grade Y were 588 insert 578 explain. PLEAS ANSWER Q1&B. THANK YOU.arrow_forwardAn 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…arrow_forward
- A study was carried out to compare the writing lifetimes of four premium brands of pens. It was thought that the writing surface might affect life- time, so three different surfaces were randomly se- tected. A writing machine was used to ensure that conditions were otherwise homogeneous (e.g., con- stant pressure and a fixed angle). The accompany- ing table shows the two lifetimes (min) obtained for each brand-surface combination. In addition, EEEr = 11,499,492 and EExj, = 22,982,552, Writing Surface 1 2 3 1 709, 659 713, 726 660, 643 Brand 2 668, 685 722, 740 692, 720 of Pen 3 659, 685 666, 684 678, 750 4 698, 650 704, 666 686, 733 4112 4227 4122 4137 5413 5621 5564 16,598 Carry out an appropriate ANOVA, and state your conclusions.arrow_forwardAssuming that for the height of women, μ = 63.83 inches and σ = 2.95 inches, find the following: a) Pr{Y > 70.5} b) Pr{Y < 55.9} c) Pr{60.5 < Y < 70.9} 3) Refer to problem (2). Give the following percentiles (use R): a) 33 b) 99.9 c) 50 d) 0.1arrow_forwardArtificial joints consist of a ceramic ball mounted on a taper. The article "Friction in Orthopaedic Zirconia Taper Assemblies" (W. Macdonald, A. Áspenberg, et al., Proceedings of the Institution of Mechanical Engineers, 2000: 685-692) presents data on the coefficient of friction for a push-on load of 2 kN for taper assemblies made from two zirconium alloys and employing three different neck lengths. Five measurements were made for each combination of material and neck length. The results presented in the following table are consistent with the cell means and standard deviations presented in the article. Тарег Material Neck Length Coefficient of Friction CPTI-ZIO2 CPTI-Z:O, CPTI-Z:O, Long TIAlloy-ZrO, Short TiAlloy-ZrO, Medium TiAlloy-ZrO, Long Short 0.254 0.195 0.281 0.289 0.220 Medium 0.196 0.220 0.185 0.259 0.197 0.329 0.481 0.320 0.296 0.178 0.150 0.118 0.158 0.175 0.131 0.180 0.184 0.154 0.156 0.177 0.178 0.198 0.201 0.199 0.210 Compute the main effects and interactions. Construct…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill