STAT 345: Design and Analysis of Experiments 2021-2022
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Department of Mathematics and Statistics
Assignment 1
STAT 345: Design and Analysis ofExperiments
2021-2022 Regular Session, Term 2
Problem 1 (30 points)
Four different designs for a digital computer circuit are being studied in order to compare the amount of noise present. The following data have been obtained:
Circuit Design Noise Observed
1 19 20 19 30 8
2 80 61 73 56 80
3 47 26 25 35 50
4 95 46 83 78 97
(a) Is the amount of noise present the same for all four designs? Use 
= 0.05.
(b) Compute a 99% confidence interval ofthe mean of circuit design 3.
(c) Compute a 95% confidence interval estimate of the mean difference between circuit designs 4 and 3. Is the amount of noise present the same for designs 3 and 4? Use 
= 0.05.
(d) Test all pairs ofmeans using the Fisher LSD method with 
= 0.05.
(e) Analyze the residuals from this experiment. Are the analysis ofvariance assumptions satisfied? (f) Which circuit design would you select for use? Low noise is best. [Hint: Figure out which designs
produce lower mean values of noise. Use (d) to check whether or not these designs differ significantly. Finally, make recommendation.]
Problem 2 (20 points)
The response time in milliseconds was determined for three different types of circuits that could be used in an automatic valve shutoff mechanism. The results from a completely randomized experiment are shown in the following table:
|
Circuit Type |
Response Time |
1 9 12 10 8 15
2 20 21 23 17 30
3 6 5 8 16 7
(a) Test the hypothesis that the three circuit types have the same response time. Use 
= 0.01. (b) Use Tukey’s test to compare pairs oftreatment means. Use 
= 0.01.
(c) If you were the design engineer and you wished to minimize the response time, which circuit type would you select?
Problem 3 (20 points)
We want to compare the effectiveness of two different pesticides, A and B, both applied in two different forms: spray (A1 and B1 ) and powder (A2 and B2). A control (that is, no pesticide), C, is included in the experiment in order to establish any effectiveness of the pesticides at all. Thus we have altogether 5 treatments: C, A1, A2, B1, B2, and each treatment is applied randomly to 2 uniformly infested plots of land. The data are given as follows:
Pesticides Observations Mean
C 12.8 13.9 13.35
The aim of the experiment and the “structure” of the treatments suggest the following comparisons:
i) control vs. pesticides,
ii) pesticide A vs. pesticide B,
iii) application A1 vs. A2,
iv) application B1 vs. B2,
v) spray vs. power,
vi) A1 vs. B1,
vii) A2 vs. B2.
(a) Define orthogonal contrasts for (i)-(iv), and carry out an orthogonal contrast analysis. (b) Define orthogonal contrasts for (i) and (v)-(vii), and carry out an orthogonal contrast analysis.
(c) Write a short paragraph to summarize your findings.
Problem 4 (20 points)
A manufacturer suspects that the batches of raw material furnished by her supplier differ significantly in calcium content. There are a large number of batches currently in the warehouse. Five of these are randomly selected for study. A chemist makes five determinations on each batch and obtains the following data:
Batch 1 Batch 2 Batch 3 Batch 4 Batch 5
(a) Is there significant variation in calcium content from batch to batch? Use 
= 0.05. (b) Estimate the components ofvariance.
(c) Find a 95 percent confidence interval for 
/(
+ 
2) and comment.
(d) Analyze the residuals from this experiment. Are the basic analysis ofvariance assumptions satisfied?
2022-02-18