RMIT Classification: Trusted
Math1302: Design and Analysis of Experiments Submit by the Due Date
Assignment 1 (100 points worth 10%) Due date: As shown on canvas
Student number: Student name:
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s1 s2 s3 s4 s5 s6 s7
INSTRUCTIONS
The following list of questions are based on the material covered in the weeks previous to the submission date. Please work through all problems using a statistical package where and if required. You will need to create a Word document to copy your outputs into and prepare your written answers to the questions below.
Submit online through Canvas by the due day.
Question 1: Discuss what is meant by the effect on a response variable.
Question 2: Differentiate between a factor and a background variable.
Question 3: Explain what constitute a treatment in a designed experiment.
Question 4: Explain what constitute random error in a designed experiment.
(4 points)
(4 points)
(4 points)
(4 points)
RMIT Classification: Trusted
(40 points) Accident statistics indicate that a substantial proportion of automobile fatalities in Australia are caused by drunken drivers. Suppose that you have been hired by an appropriate government agency to investigate the degree to which alcohol impairs one’s ability to perform automobile driving functions. Discuss what you believe are important design considerations and complete the
documentation form for your proposed experiment.
Question 5:
Question 6:
RMIT Classification: Trusted
(44 points) Photoresist is a light-sensitive material applied to semiconductor wafers so that the circuit pattern can be imaged on to the wafer. After application, the coated wafers are baked to remove the solvent in the photoresist mixture and to harden the resist. Here are measurements of photoresist thickness (in kA) for eight wafers baked at two different temperatures. Assume that all the runs were made in random order. If s3 is the third numerical digit in your student number and s7 is the seven digit in your student number then we define t=1+1.3*min(s3,s7) and q=1+1.3*max(s3,s7). Apply these number to generate the data below and use R|Rstudio|SAS to solve all the queries
11.176 q 8.097 11.739 11.291 10.759 6.467 8.315
5.263 6.748 7.461 7.015 8.133 7.418 t 8.963
(a) Is there evidence to support the claim that the higher baking temperature results in wafers with a lower mean photoresist thickness? Use 𝛼 = 0.05.
(b) What is the P-value for the test conducted in part (a)?
(c) Find a 95 percent confidence interval on the difference in means. Provide a practical
interpretation of this interval.
(d) Draw dot diagrams to assist in interpreting the results from this experiment. (e) Check the assumption of normality of the photoresist thickness.
(f) Find the power of this test for detecting an actual difference in means of 2.5 kA.
(g) What sample size would be necessary to detect an actual difference in means of 1.5 kA with a power of at least 0.9?
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