Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073530789
Author: Navidi
Publisher: MCG
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Chapter 9, Problem 17SE
The article “Factorial Experiments in the Optimization of Alkaline Wastewater Pretreatment” (M. Prisciandaro. A. Del Borghi, and F. Veglio, Industrial Engineering and Chemistry Research, 2002:5034–5041) presents the results of several experiments to investigate methods of treating alkaline wastewater. One experiment was an unreplicated 24 design. The four factors were A: concentration of sulfuric acid. B: temperature. C: time, and D: concentration of calcium chloride. The outcome variable is the amount of precipitate in kg/m3 The results are presented in the following table.
- a. Estimate all main effects and interactions.
- b. Which effects seem to be larger than the others?
- c. Assume that all third-and higher-order interactions are equal to 0, and add their sums of squares. Use the result in place of an error sum of squares to compute F statistics and P-values for the main effects. Which factors can you conclude to have an effect on the outcome?
- d. The article described some replicates of the experiment, in which the error mean square was found to be 1.04, with four degrees of freedom. Using this value, compute F statistics and P-values for all main effects and interactions.
- e. Do the results of part (d) help to justify the assumption that the third-and higher-order interactions are equal to 0? Explain.
- f. Using the results of part (d), which factors can you conclude to have an effect on the outcome?
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19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance.
19a. Step 2: Compute the df and locate the critical values.
df = _______
Critical value = ________
19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance.
19. Step 1: Which of the following is the correct set of hypotheses?A. H0: The preferences will not match production (40% Half Pint, 40% XXX, 20% Dark Knight); and H1: The preferences will match production
B. H0: \mu_{1}μ1 = \mu_{2}μ2 = \mu_{3}μ3; and H1: At least one of the categories will be different than the others
C. H0: The preferences will match production (40% Half Pint, 40% XXX, 20% Dark Knight); and H1: The preferences will not match production
19b. Step 2: Compute the df and locate the…
19. A local brewery produces three premium lagers named Half Pint, XXX, and Dark Knight. Of its premium lagers, the brewery bottles 40% Half Pint, 40% XXX, and 20% Dark Knight. In a marketing test of a sample of 80 consumers, 26 preferred the Half Pint lager, 42 preferred the XXX lager, and 12 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, test whether the production of the premium lagers matches these consumer preferences using a .05 level of significance.
19. Step 3: Compute the test statistic -- Chi-square
χ2 = (use 2 decimal places) _____________
Step 4: Decision and Conclusions
19. Step 4: Decision:
A. Reject H0
B. Retain H0
19. Step 5: Conclusion: Did the production of the premium lagers match consumer preferences?
A. Yes. The observed frequencies did not differ from the expected frequencies.
B. No. The observed frequencies differed from the expected frequencies.
Chapter 9 Solutions
Statistics for Engineers and Scientists
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