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hwk1soln - STA 8200 Design of Experiments for Research...

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STA 8200 — Design of Experiments for Research Workers Homework 1 – SOLUTION 1. A test program was conducted to evaluate how the quality of epoxy glass fiber pipes is affected by the operating conditions (Normal vs. Severe) used during their production. The test program required sixteen pipes, half of which were made at each of two manufacturing plants. Each pipe was produced under one of two operating conditions and the water temperature at which each pipe was tested was measured at the time of the test. The following table summarizes the experimental conditions for this study: Run Plant Operating Water Number Conditions Temp. ( F) 1 1 Normal 175 2 1 Normal 173 3 1 Severe 170 4 2 Severe 176 5 1 Normal 165 6 1 Normal 162 7 2 Normal 167 8 1 Severe 172 9 2 Normal 159 10 2 Severe 164 11 2 Normal 164 12 1 Severe 171 13 2 Severe 160 14 2 Severe 171 15 1 Severe 175 16 2 Normal 165 Identify which of the following statistical design features are included in the test program and what they are: (a) Treatment Factor(s), (b) Treatments, (c) Blocks, (d) Experimental Units, (e) Replications, (f) Covariates. a. Included: operating condition b. Included: normal operation and severe operation are the two treatments. c. Included: plant 1 and plant 2 are the two blocks (plant is the blocking factor). d. Included: the epoxy glass fiber pipes (the runs). There are 16 of them. e. Included: Because there are several observations at each combination of the levels of the controllable factors, we have replication here. For example, for plant 1 combined with normal operating condition we have 4 replicates (runs 1, 2, 5, and 6). f. Included: water temperature was not controlled but was measured dur- 1
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ing the collection fo the quality data. Therefore, water temperature is a covariate. 2. Do exercise 3 on p.31 of Dean and Voss. a. The objective of the experiment is to determine whether and how the boiling point of water changes with the concentration of salt in the water. b. The treatment factor here would be concentration of salt in the water. The levels to be included in the experiment depend somewhat on the populations to which the investigator wants to generalize. For example, if the goal is to determine whether there are differences in boiling points due to variabil- ity in the amount of salt concentration in tap water in US cities, then one might want to select 4 or 5, say, evenly spaced levels of salt concentration in the range 0 to the maximum salt concentration likely to be found in US tap water. If instead, for example, one were interested in whether or not differ- ences in boiling temperature exist for seawater from particular locations in the Pacific Ocean, then one would want to use the salt concentrations from those various locations. Regardless, one would almost certainly want to include a zero concentration for comparison. Experimental units might be one gallon samples of water from the same source (a single tap in a science lab). If water samples were obtained from different sources, or across dif- ferent days or locations, then source, day, location would become nuisance sources of variablity that should be blocked for in the design. It would be
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