12.64

Material and labor costs. Many companies must accurately estimate their costs before a job is begun in order to acquire a contract and make a profit. For example, a heating and plumbing contractor may base cost estimates for new homes on the total area of the house and whether central air conditioning is to be installed.

1. Write a main effects model relating the mean cost of material and labor, E(y) , to the area and central air conditioning variables.
2. Write a complete second-order model for the mean cost as a function of the same two variables.
3. What hypothesis would you test to determine whether the second-order terms are useful for predicting mean cost?
4. Refer to part c. The contractor samples 25 recent jobs and fits both the complete second-order model (part b) and the reduced main effects model (part a), so that a test can be conducted to determine whether the additional complexity of the second-order model is necessary. The resulting SSE and R ² values are shown in the table. Is there sufficient evidence to conclude that the second-order terms are important for predicting the mean cost? Use \(\alpha =.05\).

12.66

Carbon dioxide flooring experiment. One of the most promising methods for extracting crude oil employs a carbon dioxide (CO ₂ ) flooding technique. CO ₂ when flooded into oil pockets enhances oil recovery by displacing the crude oil. In a microscopic investigation of the CO ₂ flooding process, flow tubes were dipped into sample oil pockets containing a known amount of oil. The oil pockets were flooded with CO ₂ and the percentage of oil displaced was recorded. The experiment was conducted at three different flow pressures and three different dipping angles. The displacement test data are recorded in the accompanying table. (file: CO2FLOOD)

1. Write a complete second-order model relating percentage oil recovery y to pressure x ₁ and dipping angle x ₂ .
2. Plot the sample data on a scattergram, with percentage oil recovery y on the vertical axis and pressure x ₁ on the horizontal axis. Connect the points corresponding to the same value of dipping angle x ₂ . Based on the scattergram, do you believe a complete second-order model is appropriate?
3. Fit the interaction model \[y={{\beta }_{0}}+{{\beta }_{1}}{{x}_{1}}+{{\beta }_{2}}{{x}_{2}}+{{\beta }_{3}}{{x}_{1}}{{x}_{2}}+\varepsilon \] to the data. Give the least-squares prediction equation.
4. Construct a plot similar to the scattergram of part b , but use the predicted values from the interaction model on the vertical axis. Compare the two plots. Do you believe the interaction model will provide an adequate fit?
5. Check model adequacy using a statistical test with \[\alpha =.05\] .
6. Is there evidence of interaction between pressure x ₁ and dipping angle x ₂ ? Test using \[\alpha =.05\] .

12.75

In order to do a multiple regression, you need to select a set of variables to begin collecting data on. How do you determine which variables to use at the start. What types of things do you think should be considered? Give examples.

13.22

Factorial experiment. Consider a two-factor factorial experiment where one factor is set at two levels and the other factor is set at four levels. How many treatments are included in the experiment? List them.

14.62

Concentration of trace elements. Vanadium (V) is a recently recognized essential trace element. An experiment was conducted to compare the concentrations of V in biological materials using isotope dilution mass spectrometry. The accompanying table gives the quantities of V (measured in nanograms per gram) in dried samples of oyster tissue, citrus leaves, bovine liver, and human serum. (file: VANADIUM)

1. Identify the treatments in this experiment.
2. Is there sufficient evidence (at \[\alpha =.05\] ) to indicate that the mean V concentrations differ among the four biological materials?
3. If appropriate, use a multiple comparisons procedure to rank the treatment means at \[\alpha =.06\] .

14.64

Comparing insecticides. A species of Caribbean mosquito is known to be resistant against certain insecticides. The effectiveness of five different types of insecticides (temephos, malathion, fenitrothion, fenthion, and chlorpyrifos) in controlling this mosquito species was investigated in the Journal of the American Mosquito Control Association. Mosquito larvae were collected from each of seven Caribbean locations. In a laboratory, the larvae from each location were divided into five batches and each batch was exposed to one of the five insecticides. The dosage of insecticide required to kill 50% of the larvae was recorded and divided by the known dosage for a susceptible mosquito strain. The resulting value is called the resistance ratio. (The higher the ratio, the more resistant the mosquito species is to the insecticide relative to the susceptible mosquito strain.) The resistance ratios for the study are listed in the next table. The researchers wanted to compare the mean resistance ratio of the five insecticides. (file: MOSQUITO2)

1. Explain why the experimental is a randomized block design. Identify the treatments and the blocks.
2. Conduct a complete analysis of the data. Are any of the insecticides more effective than any of the others?

14.70

Coal ash study. The data shown in the table below are the results of an experiment conducted to investigate the effect of three factors on the percentage of ash in coal. (file: COALASH)

The three factors, each at four levels, were:

Type of coal (factor A): Majiri, Michael, Kairan, and Metallurgical coke.

Maximum partical size (factor B): 246, 147, 74, and 48 microns.

Weight of selected coal specimen (factor C): 1 gram, 100 milligrams, 20 milligrams, and 5 milligrams.

Three specimens were prepared for each of the \[4\times 4\times 4=64\] factor-level combinations, yielding three replications of a complete \[4\times 4\times 4\] factorial experiment.

1. Set up an analysis of variance table showing the sources and degrees of freedom for each.
2. Do the data provide evidence of any interactions among the factors? Test using \[\alpha =.05\] .
3. Does the mean level of coal ash obtained in the analysis depend on the weight of the coal specimen? Test using \[\alpha =.05\] .
4. Find 95% confidence intervals for the difference in the mean ash content between Majiri and Michel coal at each of the four levels of maximum particle size.

14.77

A single can of dried eggs was stirred well. Samples were drawn and a pair of samples (claimed to be of two "types"), was sent to each of six commercial laboratories to be analyzed for fat content. Each laboratory assigned two technicians, who each analyzed both "types". Since the data were all drawn from a single well-mixed can, the null hypothesis for ANOVA that the mean fat content of each sample is equal is true. The experiment is thus really a study of the laboratories. Your job is to analyze these data using what you have learned. Give a summery of your conclusions with graphs and output. (file: FAT)

Variable Names:

1. Fat content: Fat content as a percentage.
2. Lab: Lab which ran the experiment, expressed as a roman numeral I-VI.
3. Technician: Technician number (either 1 or 2).
4. Sample: Sample type used (these are the labels given to the labs, however they were really of the same stuff).

Price: $35.93

Solution: The downloadable solution consists of 17 pages, 1893 words and 14 charts.
Deliverable: Word Document