Smokestack scrubbers
Particulate matter is a serious form of air pollution often arising from industrial produc- tion. One way to reduce the pollution is to put a filter, or scrubber, at the end of the smokestack to trap the particulates. An experiment to determine which smokestack scrubber design is best was run by placing four scrubbers of different designs on an industrial stack in random order. Each scrubber was tested 5 times. For each run, the same material was produced, and the particulate emissions com- ing out of the scrubber were measured (in parts per billion).
Level n Mean StdDev
1 20 4.80000 4.57223
2 21 9.61905 4.12888
3 36 6.52778 3.83582
a) What kind of design or study is this?
b) What are the null and alternative hypotheses?
c) What does the ANOVA table say about the null hypoth- esis? (Be sure to report this in terms of sugar content and shelf placement.)
Dependent Variable: SUGARS
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I) SHELF
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J) SHELF
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Mean Difference (I-J)
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Std. Error
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P-value
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95% Confidence Interval
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Bonferroni
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Lower Bound
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Upper Bound
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1
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2
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- 4.819
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1.2857
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0.001
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- 7.969
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- 1.670
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|
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3
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- 1.728
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1.1476
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0.409
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- 4.539
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1.084
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2
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1
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4.819
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1.2857
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0.001
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1.670
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7.969
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|
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3
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3.091
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1.1299
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0.023
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0.323
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5.859
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|
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3
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1
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1.728
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1.1476
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0.409
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- 1.084
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4.539
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|
|
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2
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- 3.091
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1.1299
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0.023
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- 5.859
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- 0.323
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d) Can we conclude that cereals on shelf 2 have a different mean sugar content than cereals on shelf 3? Can we con- clude that cereals on shelf 2 have a different mean sugar content than cereals on shelf 1? What can we conclude?
e) To check for significant differences between the shelf means, we can use a Bonferroni test, whose results are shown here. For each pair of shelves, the difference is shown along with its standard error and significance level. What does it say about the questions in part d?