1. Problems

2. 1.The tensile strength of concrete produced by 4 mixer levels is being studied. The data are: Compute the MS for the mixers and plot the means. Is there a difference among them? For the greatest tensile strength, which mixer would you choose? Mixer 1 Mixer 2Mixer 3Mixer 4 Rep 120304525 Rep 220354525 Rep 325 5020 Rep 415304030

3. 2.For the data in problem 1, compute MS(error) and the F-ratio and do the ANOVA table.

4. 3. Here are the cell and marginal means from an experiment. According to the ANOVA table, the A and B main effects and the AB interaction are all significant. If your objective is to minimize the response, which values of A and B would you select. Explain. B low B highA marg A low551535 A high253530 B marg402532.5

5. 4. A textile mill has a large number of looms to weave its cloth. At random, 3 looms are chosen to see if the looms are meeting the standard cloth output. The data are What type of ANOVA is this? Do the ANOVA to see if there is any real variability among the looms. Loom 1Loom 2Loom 3 Rep 112 11 Rep 2141312 Rep 3161413

6. 5. The E(MS) for the A effect is (a) What type of factor is this? (b) How many factors are in the model? (c) How would you set up the F-test?

7. 6. Because of limited resources, an experiment with 4 factors at 2 levels each is placed in an 8-run design. (a) What kind of design is it? (b) What is its generator? (c) What is the design resolution? (d) List all confounded effects.

8. 7. Three different circuit designs are being studied to find the least amount of noise present. The data are (a) How many replications does this experiment have? (b) Do the ANOVA. (c) Find the best circuit design. Circuit Design Noise present A231 B567 C435

9. 8. The effects of a 2 x 2 fixed effects factorial design are: A effect = 1 B effect = -9 AB effect = -29 = 30.5 (a) Write the fitted regression model for this design. (b) Plot the interaction effect.

10. 9.A factory produces grain refiners in 3 different furnaces, each of which has its own unique operation characteristics. Each furnace can be run at 3 different stirring rates. The process engineer knows that stirring rate affects the grain size of the product, so he decides to run an experiment testing the three stirring rates on his 3 furnaces. (a) What type of design is this? Why? (b) Set up the experiment.

11. 10. The effect of 5 different ingredients on reaction time is being studied. Each batch of material is large enough for only 5 runs. Moreover, only 5 runs can be made in a day. Design the experiment.

12. 11. The yield of a chemical process is being studied using 5 batches of raw material and 5 acid concentrations, which are nuisance factors. Two factors are suspected to be important: standing time (5 levels) and type of catalyst (5 levels). (a) What kind of experiment is this? (b) Design the experiment.

13. 12. The mean results for a completely balanced experiment are With these cells means, compute orthogonal contrasts and their SS for: (a) High Pressure vs the average of Low and Medium Pressure. (b) Low Pressure vs Medium Pressure (c) Medium Pressure vs High Pressure Pressure TemperatureLowMediumHigh Low 768 Medium 6513 High 111015

14. 13. A semiconductor engineer is studying the effect of lamination temperature (55˚C and 75˚C), lamination time (10 seconds and 25 seconds), lamination pressure (5 tn and 10 tn), and firing temperature (1580˚C and 1620˚C) on the curvature of the substrates produced. He must finish his study in one day so he can do only 8 runs. He is not very good at experimental design and doesn’t know how to do it. You are his statistical consultant and he asks you to design an experiment for him. Design the experiment and explain what problems he will have after he gets his results.