Lab session 2: Questions
Question 1: The effect of three different lubricating oils on fuel economy in diesel truck engines is being studied. Fuel economy is measured using brake-specific fuel consumption after the engine has been running for 15 minutes. Five different truck engines are available for the study, and the experimenters conduct the following randomized complete block design.
a) Create a data frame called ¡°Fuel¡± in R to store the above data. Use str() command to display the structure of the data.
b) Analyse the data from this experiment. State your hypotheses (use ¦Á = 5%) and draw conclusions.
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c) Construct the confidence intervals for each factor (for each level). Comment on the significance of the effect of each level based on this interval.
d) Use the Fisher LSD method to make comparisons among the three lubricating oils to determine specifically which oils differ in brake-specific fuel consumption.
e) Analyse the residuals from this experiment and comment on model adequacy.
Question 2: The effect of five different ingredients (A, B, C, D, E) on the reaction time of a chemical process is being studied. Each batch of new material is only large enough to permit five runs to be made. Furthermore, each run requires approximately 1 and 1/2 hours, so only five runs can be made in one day. The experimenter decides to run the experiment as a Latin square so that day and batch effects may be systematically controlled. She obtains the data that follow.
2 C =11 E = 2
D=1 C=7 A=7 D=3 C =10 E=1 E=6 B=6 B=3 A=8
E=3 B=8 D=5 A =10 C=8
a) Use the ANOVA table to decide whether the five treatments are different. State your hypotheses and draw conclusions.
b) Are the blocking factors significant?
c) Compare all pairs of treatment means by using either the Fisher or the Tukey tests.
d) Suppose that there is an additional source of variation. A fourth factor in five levels,
workplace (¦Á, ¦Â, ¦Ã, ¦Ä, ¦Å), needs to be considered.
– What design should we employed and how the new experiment will look like. – Test whether the new factor is significant in this new design.
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