Stat 722 Assignment # 8
1. Some tests were carried out on a newly designed carburetor. Four variables were studied as follows:
Copyright By PowCoder代写 加微信 powcoder
Variable Description – + _
Spring tension
Aperture Size
Gas flow rate
The immediate objective was to find the effects of these changes on the amount of unburned hydrocarbons in the engine exhaust gas. The following results were obtained from a 24-1 design:
Run A B C D Unburned hydrocarbons
1 – + + + 8.2
2 – – + – 1.7
3 – – – + 6.2
4 + – – – 3.0
5 + – + + 6.8
6 + + + – 5.0
7 – + – – 3.8
8 + + – + 9.3
The researcher wants to find a combination of A, B, C, and D that will minimize the levels of unburned hydrocarbons. Analyze this data using an appropriate modification of Yates’ method. Use the results of this analysis to make some recommendations about further experiments that might be conducted.
2. A 1/4 fraction of a 26 factorial design was used to study the effects of some variables on an operating chemical process. The effects used to define the 1/4 replicate were the ABCE and BCDF effects. The variables are defined by:
Variable Description 0 1 _
Ctlyst Concentration
NaOH Concentration
Agitation Speed
Temperature
The data that was obtained is shown below:
Run A B C D E F impurity
2 0 0 0 0 0 0 0.38
6 1 0 0 0 1 0 0.40
12 0 1 0 0 1 1 0.27
4 1 1 0 0 0 1 0.30
1 0 0 1 0 1 1 0.58
7 1 0 1 0 0 1 0.56
14 0 1 1 0 0 0 0.30
3 1 1 1 0 1 0 0.32
8 0 0 0 1 0 1 0.59
10 1 0 0 1 1 1 0.62
15 0 1 0 1 1 0 0.53
11 1 1 0 1 0 0 0.50
16 0 0 1 1 1 0 0.79
9 1 0 1 1 0 0 0.75
5 0 1 1 1 0 1 0.53
13 1 1 1 1 1 1 0.54
a) Calculate the (standardized) effects that are estimable from these data using Yates’ algorithm.
b) Construct a half normal plot of the standardized effects.
c) Which effects appear to be statistically significant?
d) Provide an estimate of σ.
e) It is important to reduce impurity. Interpret your results with this in mind.
f) The researcher is going to run some additional experiments. What recommendations would you make in order to help the researcher minimize impurity?
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com