1. A 24 experiment was conducted in a CR design to study the effect load on drill (A), flow rate through drill (B), rotational speed (C), and mud used in drilling(D), has on the rate of advance of a stone drill and the following data were gathered.
(a) Use SAS or JMP to obtain the ANOVA for the above model. Copy and paste the ANOVA table, including the tests of treatment combination means, interactions, and main effects. If using SAS, please make sure you paste Type III Sum of squares. Also determine, at 0.05 significance level, if at least one treatment combination mean is significantly different from the others.
(b) Test whether there are significant interactions and main effects (at 0.05 level) and fill in your findings in the following table. Please also state whether you should have carried out each of these tests or not and the reasons for each such answer.
(c) Except for Mud (D), all factors are quantitative. If you are interested in finding how to maximize drill advance rate, what would you do next?
2. describes an experiment conducted in a CR design to investigate the effect of Type of glass and the Type of phosphor on the brightness of a television tube. The response variable is the current necessary (in micro-amps) to obtain the specific brightness level (lower values are better). The data from this experiment is given below (this is Problem 5.6 in Text but some data points have been changed).
Do the following:
(a) Carry out an analysis of variance using SAS or JMP and copy and paste below, the ANOVA table including the Type III SS (if you used SAS) for the treatment combinations, the main effects and the interaction term.
(b) Carry out a test to determine if the treatment combination means are equal or not, a 0.05 significance level. State your conclusions.
(c) Test whether the interaction terms are different from zero or not at the 0.05 significance level. State and justify your conclusion and write down any results from the SAS/JMP output you used in coming to your conclusion.
Should you have done this test in light of the results you obtained in part (b)?
(d) Test whether the main effects (of both Glass Type and Phosphor Type) are significantly different from zero or not using the 0.05 significance level. State and justify your conclusions and write down any results from the SAS output you used. Should you have done this test in light of the results you obtained in part (c)?
(e) Conduct an LSD test to determine which combination of factor levels is best at producing the required brightness at the lowest current level. This test can be on treatment combination means or on the main effect means depending whether or not the interaction is significant. Copy and paste results below. State your conclusions.
3. Please see Problem 4.11 in the Chapter 4 problem pages. Please consider “Project” as a blocking factor and “Algorithm” as the single experimental variable of interest.
(a) Carry out an analysis of variance for this one-way experiment in an RCB design and copy and paste the complete ANOVA table below. Please use JMP. Please show the sum of squares due to blocks as well as the single factor.
(b) Using the above AOVA results determine if there are significant differences among (i) the blocks and (ii) among the population mean accuracy of cost estimates of the algorithms. State the reasons for each of the conclusions (use the ANOVA results to justify your answer). Please use 0.05 significance level.
(c) Compare the six means associated with the algorithms using Tukey’s test. Copy and paste the results below. State your conclusions.
(d) Test, using an appropriate contrast that the average of the population means associated with the three COCOMO algorithms is different from the average of the population means associated with the other three algorithms.
(e) Test, using an appropriate contrast that the population mean associated with the FUNCTION POINTS algorithm is different from the population mean associated with the ESTIMALS algorithm.
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