IE7280 Final Exam Fall 2021
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IE7280 Final Exam
Fall 2021
1. (30 points) A research engineers for a tire manufacturer is investigating tire life for a new rubber compound. He has built 16 tires and tested them to end-of-life KM in a road test. The test data yields: sample mean = 54 KM and sample standard deviation 3.645. (Use α = 0.05)
a) Can you conclude that the population mean is at least 57 KM?
b) What is the maximum error of estimation.
c) What sample size will be required, if the maximum error (from your result of part b)must be reduced to half? Use maximum error of 0. 10, if you do not have any reasonable result for part b.
2. (35 points) Use the Minitab Output below to answer the following questions. (Use a = 0.05)
Predictor
Constant
x1
x2
|
|
R2 = |
|
SE Coef |
T |
P |
|
1.007 |
3.290 |
0.003 |
0.5768
0.6571
R2adj =
Analysis of Variance
Source Regression Residual Error
Total
DF
2
|
|
27
SS
133.366
17.332
150.698
MS
66.683
a) Find all of the missing values.
b) Find the estimate of G 2 .
c) Test for significance of regression
d) Test for significance of F1 and F2 with t-test. Comment on the two results.
e) Construct a 95% CI on F1 . Use this CI to test for significance of F1 .
f) Construct a 95% CI on F2 . Use this CI to test for significance of F2 .
g) Comment on results found in parts (c)-(f). Is this regression model appropriate? What is your recommended next step in the analysis.
3. (35 points) A particular county employs three assessors who are responsible for determining the value of residential property in the county. To see whether these assessors differ systematically in their assessments, 5 houses are selected, and each assessor is asked to determine the market value of each house. With factor A denoting assessors (I=3) and factor B denoting houses (J=5), suppose SSA=11.7,SSB=113.5, and SSE=25.6. (Use α = 0.05)
a) Test H0: G1 = G2 = G3 . (H0 states that there are no systematic differences among assessors) .
b) Set up null and alternative hypotheses for blocking, and test for blocking.
c) Explain why a randomized block experiment with only 5 houses was used rather than a one- way ANOVA experiment involving a total of 15 different houses, with each assessor asked to assess 5 different houses (a different group of 5 for each assessor) .
2022-12-09