Homework answers / question archive / 3

3

Statistics

Share With

---

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:

Mixing Technique                                   Tensile Strength (Ib/in2)
1	3129	3000	2865	2890
2	3200	3300	2975	3150
3	2800	2900	2985	3050
4	2600	2700	2600	2765

 

 (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.

Dosage                                                                       Observations
20g	24	28	37	30
30g	37	44	31	35
40g	42	47	52	38

 

 (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:

Material                                                                           Failure Time (minutes)
1	110	157	194	178
2	1	2	4	18
3	880	1256	5276	4355
4	495	7040	5307	10,050
5	7	5	29	2

 

 (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.