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5 5.7 Problems 229 Device Brand of DVD Battery Radio Camera Player A B (a) Analyze the data and draw conclusions, using (b) Investigate model adequacy by plotting the residuals. (c) Which brand of batteries would you recommend? I have recently purchased new golf clubs, which I believe will significantly improve my game. Below are the scores of three rounds of golf played at three different golf courses with the old and the new clubs. Course Clubs Ahwatukee Karsten Foothills Old New (a) Conduct an analysis of variance. Using 0.05, what conclusions can you draw? (b) Investigate model adequacy by plotting the residuals A manufacturer of laundry products is investigating the performance of a newly formulated stain remover. The new formulation is compared to the original formulation with respect to its ability to remove a standard tomato-like stain in a test article of cotton cloth using a factorial experiment. The other factors in the experiment are the number of times the test article is washed (1 or 2) and whether or not a detergent booster is used. The response variable is the stain shade after washing (12 is the darkest, 0 is the lightest). The data are shown in the following table. Number of Number of Washings Washings 1 2 Formulation Booster Booster Yes No Yes No New 6, 5 6, 5 3, 2 4, 1 Original 10, 9 11, 11 10, 9 9, 10 (a) Conduct an analysis of variance. Using 0.05, what conclusions can you draw? (b) Investigate model adequacy by plotting the residuals Bone anchors are used by orthopedic surgeons in repairing torn rotator cuffs (a common shoulder tendon injury among baseball players). The bone anchor is a threaded insert that is screwed into a hole that has been drilled into the shoulder bone near the site of the torn tendon. The torn tendon is then sutured to the anchor. In a successful operation, the tendon is stabilized and reattaches itself to the bone. However, bone anchors can pull out if they are subjected to high loads. An experiment was performed to study the force required to pull out the anchor for three anchor types and two different foam densities (the foam simulates the natural variability found in real bone). Two replicates of the experiment were performed. The experimental design and the pullout force response data are as follows. Foam Density Anchor Type Low High A 190, , 255 B 185, , 237 C 210, , 260 (a) Analyze the data from this experiment. (b) Investigate model adequacy by constructing appropriate residual plots. (c) What conclusions can you draw? An experiment was performed to investigate the keyboard feel on a computer (crisp or mushy) and the size of the keys (small, medium, or large). The response variable is typing speed. Three replicates of the experiment were performed. The experimental design and the data are as follow. Keyboard Feel Key Size Mushy Crisp Small 31, 33, 35 36, 40, 41 Medium 36, 35, 33 40, 41, 42 Large 37, 34, 33 38, 36, 39 (a) Analyze the data from this experiment. (b) Investigate model adequacy by constructing appropriate residual plots. (c) What conclusions can you draw? An article in Quality Progress (May 2011, pp ) describes the use of factorial experiments to improve a silver powder production process. This product is used in conductive pastes to manufacture a wide variety of products ranging from silicon wafers to elastic membrane switches. Powder density (g/cm 2 ) and surface area (cm 2 /g) are the two critical

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