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3.7 The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected:

 (a) Test the hypothesis that mixing techniques affect the strength of the cement. Use a = 0.05.

(b) Construct a graphical display as described in Section 3.5.3 to compare the mean tensile strengths for the four mixing techniques. What are your conclusions?

(c) Use the Fisher LSD method with a = 0.05 to make comparisons between pairs of means.

(d) Construct a normal probability plot of the residuals. What conclusion would you draw about the validity of the normality assumption?

(e) Plot the residuals versus the predicted tensile strength. Comment on the plot.

(f) Prepare a scatter plot of the results to aid the interpretation of the results of this experiment.

3.12. A pharmaceutical manufacturer wants to investigate the bioactivity of a. new drug. A completely randomized single-factor experiment was conducted with three dosage levels, and the following results were obtained.

 (a) Is there evidence to indicate that dosage level affects bioactivity? Use a = 0.05.

(b) If it is appropriate to do so, make comparisons between the pairs of means. What conclusions can you draw?

(c) Analyze the residuals from this experiment and comment on model adequacy.

3.28  An experiment was performed to investigate the effectiveness of five insulating materials. Four samples of each material were tested at an elevated voltage level to accelerate the time to failure. The failure times (in minutes) are shown below:

 (a) Do all five materials have the same effect on mean fail-ure time?

(b) Plot the residuals versus the predicted response. Construct a normal probability plot of the residuals. What information is conveyed by these plots?

(c) Based on your answer to part (b) conduct another analysis of the failure time data and draw appropriate conclusions.