Refer to Exercise 18.36.
a. Estimate the size of the variance associated with each of the random factors in the study.
b. Provide the proportions of the total variation associated with each of the sources of random variation in the study.
c. Is the amount of variation in the quantity of NaNO2 across the runs consistent for the three quality levels?
In Exercises 18.39–18.42, describe the experimental situations by provide the following information:
1. Identify the type of randomization (completely randomized design, randomized complete block design, Latin square design, split-plot, crossover, etc.).
2. Identify the type of treatment structure (single factor, crossed factors, nested factors, fractional, etc.).
3. Identify each of the factors as being fixed or random.
4. Describe the experimental units and measurement units.
5. Describe the measurement process: response variable, covariates, subsampling, and repeated measures.
6. Provide a partial AOV table containing just sources of variation and degrees of freedom.
Sodium nitrate, a preservative that is used in some processed meats, such as bacon, jerky, and luncheon meats, could increase your heart disease risk. A consumer protection organization is evaluating the level of sodium nitrate (NaNO2) from sausages obtained from the three largest food processors—P1, P2, and P3—in the United States. Each manufacturer produces three grades of quality for their sausage—Q1, Q2, and Q3. The processing of different grades of sausage from a common production run may involve different sources of raw materials and processing environments, and these factors sometimes are problematic. Each food processor submits two sausages of each grade from each of three production runs. The amount of NaNO2 is determined and is reported in the following table. The three food processors are the only processors under evaluation, the production runs were randomly selected and are representative of general production runs of each food processor.
a. What type of randomization was utilized in this experiment (completely randomized design, randomized complete block design, Latin square design, etc.)?
b. What type of treatment structure was used (single factor, crossed factors, nested factors, etc.)?
c. Identify each of the factors as being fixed or random.
d. Describe the experimental units for each factor and the measurement units.
e. Write a statistical model for this experiment, and include all necessary conditions on the model parameters and variables.
A research specialist for a large seafood company investigated bacterial growth on oysters and mussels subjected to three different storage temperatures. Nine cold storage units were available. Three storage units were randomly assigned to be used for each of the storage temperatures: 0, 5, and 10°C. Oysters and mussels were stored for 2 weeks in each of the cold storage units. A bacterial count was made from a sample of oysters and a sample of mussels from each storage unit at the end of 2 weeks, so that for each storage unit there is a bacterial value for oysters and a bacterial value for mussels, yielding a total of 18 observations.
An industrial engineer is studying the hand insertion of electronic components on printed circuit boards in order to improve the speed of the assembly operation. She has designed three assembly fixtures (F1, F2, and F3) and two workplace layouts (Ll and L2) that seem promising. Specialized operators are required to perform the assembly, and it was initially decided to randomly select four operators from the many qualified operators at the plant. However, because the workplaces are in different locations within the plant, it is difficult to use the same operators for each layout. Therefore, the four operators randomly chosen for layout 1 are different individuals from the four operators randomly chosen for layout 2. Each of the operators assembles 4 circuit boards for each of the three fixture types, with the 12 circuit boards assembled in random order. The 96 assembly times are measured in seconds. The engineer is interested in the effects of assembly fixtures (F), workplace layout (L), and operator (O) on the average time required to assemble the circuit boards.
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