The article "Experimental Design Approach for the Optimization of the Separation of Enantiomers in Preparative Liquid Chromatography" (S. Lai and Z. Lin, Separation Science and Technology, 2002: 847–875) describes an experiment involving a chemical process designed to separate enantiomers. A model was fit to estimate the cycle time (y) in terms of the flow rate (x1), sample concentration (x2), and mobile-phase composition (x3). The results of a least-squares fit are presented in the following table. (The article did not provide the value of the t statistic for the constant term.) Predictor Coefficient т Constant 1.603 X1 -0.619 -22.289 0.000 X2 0.086 3.084 0.018 0.306 11.011 0.000 0.272 8.542 0.000 0.057 1.802 0.115 0.105 3.300 0.013 X1X2 -0.022 -0.630 0.549 XXз -0.036 -1.004 0.349 X>Xз 0.036 1.018 0.343 Of the following, which is the best next step in the analysis? i. Nothing needs to be done. This model is fine. Drop x;, x;, and x from the model, and then perform an F test. iii. Drop x1x2, X1X3,and x2x3 from the model, and then perform an F test. iv. Drop x, and x; from the model, and then perform an F test. Add cubic terms x, x, and x} to the model to try to improve the fit. ii. V.

Preliminary data analysis indicate that it is reasonable to use a t-test to carry out the specified hypothesis test. Perform the t-test using the critical-value approach. %3D X = 44.2 and s = 7.3 Use a significance level of a = 0.05 to test the claim that u 35.8. The sample data consists of 10 scores for which H:µ±35.8 0 Н и-35.8 Test statistics: t=3.64 Critical Value: t=+/-2.262 H:µ=35.8 Reject There is sufficient evidence to support the claim that the mean is different from 35.8. П. : и 3 44.2 0. H:µ±44.2 a. Test statistics: t=3.64 Critical Value: t= +/- 2.262 H:µ=44.2 Н, There is sufficient evidence to support the claim that the mean is different from 44.2. Reject

In "Orthogonal Design for Process Optimization and Its Application to Plasma Etching" (Solid State Technology, May 1987), G. Z. Yin and D. W. Jillie describe an experiment to determine the effect of C,F. flow rate on the uniformity of the etch on a silicon wafer used in integrated circuit manufacturing. Three flow rates are used in the experiment, and the resulting uniformity (in percent) for six replicates is shown below. Observations C2F, Flow (SCCM) 2 3 4 125 2.7 4.6 2.6 3.0 3.2 3.8 160 4.9 4.6 5.0 4.2 3.6 4.2 200 4.6 3.4 2.9 3.5 4.1 5.1 Use Fisher's LSD method with a = 0.05 to analyze the means of the three flow rates. Choose the correct answer. O There are significant differences between levels 125 and 160. O There are significant differences between levels 125 and 200. O There are significant differences between levels 160 and 200. O There are significant differences between levels 125 and 160, 160 and 200. O No significant differences.

An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: ... x = Temperature (°C) | 1100 1200 1300 1100 1500 1200 1300 y - Porosity (%) 30.8 19.2 6 13.5 11.4 7.7 3.6 Find an estimate of o2 Input answers up to two decimal places. o2= Blank 1

The article "Effect of Microstructure and Weathering on the Strength Anisotropy of Porous Rhyolite" (Y. Matsukura, K. Hashizume, and C. Oguchi, Engineering Geology, 2002:39- 17) investigates the relationship between the angle betwween cleavage and flow structure and the strength of porous rhyolite. Strengths (in MPa) were measured for a mumber of specimens cut at various angles. The mean and standard deviation of the strengths for each angle are presented in the following table. Angle Mean 0° 22.9 Sample Size Standard Deviation 2.98 12 15° 22.9 1.16 30° 19.7 3.00 45° 14.9 2.99 60° 13.5 2.33 75° 11.9 2.10 90 14.3 3.95 6. Can you conclude that strength varies with the angle?

Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. %3D Everest climbers (summit 29,028 feet). (units: mm Hg/10) (units: mm Hg/10) 7.3 4.6 4.2 3.3 2.1 42.4 31.7 26.2 16.2 13.9 (a) Verify that Ex = 21.5, Ey = 130.4, Ex = 107.39, Ey = 3944.74, Exy = 648.03, andr 0.969. Σχ 21.5 %3D %3D Ey 130.4 Ex2 | 107.39 Ey2 3944.74 Exy 648.03 r0.9686 (b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.) t 6.79 critical t 1.6377 Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is…

Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. Everest climbers (summit 29,028 feet). (units: mm Hg/10) (units: mm Hg/10) 3.3 x 6.7 Ly 42.2 4.9 4.2 2.1 31.7 26.2 16.2 13.9 (a) Verify that Ex = 21.2, Ey = 130.2, Ex? = 101.84, Ey? = 3927.82, Exy = 630.76, and r= 0.982. Ir = Ex 21.2 Ey 130.2 Ex2 101.84 Ey2 3927.82 Exy 630.76 r 0.982 (b) Use a 10% level of significance to test the claim that p > 0. (Use 2 decimal places.) t 9.01 critical t 1.64 Conclusion O Reject the null hypothesis, there is sufficient evidence thatp >0. O Reject the null hypothesis, there is…